NEA Nuveen AMT Free Quality Municipal Income Fund

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Check each box that appropriately characterizes the Registrant:

This post-effective amendment will become effective immediately pursuant to Rule 462(d).

EXPLANATORY NOTE

This Post-Effective Amendment No. 1 to the Registration Statement on Form N-2 (File Nos. 333-252927 and 811- 21213) of Nuveen AMT-Free Quality Municipal Income Fund (the “Registration Statement”) is being filed pursuant to Rule 462(d) under the Securities Act of 1933, as amended (the “Securities Act”), solely for the purpose of filing exhibits to the Registration Statement. Accordingly, this Post-Effective Amendment No. 1 consists only of a facing page, this explanatory note and Part C of the Registration Statement on Form N-2 setting forth the exhibits to the Registration Statement. This Post-Effective Amendment No. 1 does not modify any other part of the Registration Statement. Pursuant to Rule 462(d) under the Securities Act, this Post-Effective Amendment No. 1 shall become effective immediately upon filing with the Securities and Exchange Commission. The contents of the Registration Statement are hereby incorporated by reference.

Reference is made to the Underwriting Agreement and Dealer Agreements (or forms thereof) which relate to the specific issuances of Preferred Shares under the Registration Statement and filed or to be filed as exhibits to the Registration Statement. Reference also is made to the information under the headings “Plan of Distribution” in the Registrant’s prospectus and under the heading “Underwriting,” or other similar such captions, in the Registrant’s prospectus supplement relating to specific issuances of Preferred Shares filed with the Securities and Exchange Commission from time to time.

None.

Part C-5

Section 4 of Article XII of the Registrant’s Declaration of Trust provides as follows:

Subject to the exceptions and limitations contained in this Section 4, every person who is, or has been, a Trustee, officer, employee or agent of the Trust, including persons who serve at the request of the Trust as directors, trustees, officers, employees or agents of another organization in which the Trust has an interest as a shareholder, creditor or otherwise (hereinafter referred to as a “Covered Person”), shall be indemnified by the Trust to the fullest extent permitted by law against liability and against all expenses reasonably incurred or paid by him in connection with any claim, action, suit or proceeding in which he becomes involved as a party or otherwise by virtue of his being or having been such a Trustee, director, officer, employee or agent and against amounts paid or incurred by him in settlement thereof.

No indemnification shall be provided hereunder to a Covered Person:

(a) against any liability to the Trust or its Shareholders by reason of a final adjudication by the court or other body before which the proceeding was brought that he engaged in willful misfeasance, bad faith, gross negligence or reckless disregard of the duties involved in the conduct of his office;

(b) with respect to any matter as to which he shall have been finally adjudicated not to have acted in good faith in the reasonable belief that his action was in the best interests of the Trust; or

(c) in the event of a settlement or other disposition not involving a final adjudication (as provided in paragraph (a) or (b)) and resulting in a payment by a Covered Person, unless there has been either a determination that such Covered Person did not engage in willful misfeasance, bad faith, gross negligence or reckless disregard of the duties involved in the conduct of his office by the court or other body approving the settlement or other disposition or a reasonable determination, based on a review of readily available facts (as opposed to a full trial-type inquiry), that he did not engage in such conduct:

(i) by a vote of a majority of the Disinterested Trustees acting on the matter (provided that a majority of the Disinterested Trustees then in office act on the matter); or

(ii) by written opinion of independent legal counsel.

The rights of indemnification herein provided may be insured against by policies maintained by the Trust, shall be severable, shall not affect any other rights to which any Covered Person may now or hereafter be entitled, shall continue as to a person who has ceased to be such a Covered Person and shall inure to the benefit of the heirs, executors and administrators of such a person. Nothing contained herein shall affect any rights to indemnification to which Trust personnel other than Covered Persons may be entitled by contract or otherwise under law.

Expenses of preparation and presentation of a defense to any claim, action, suit or proceeding subject to a claim for indemnification under this Section 4 shall be advanced by the Trust prior to final disposition thereof upon receipt of an undertaking by or on behalf of the recipient to repay such amount if it is ultimately determined that he is not entitled to indemnification under this Section 4, provided that either:

(a) such undertaking is secured by a surety bond or some other appropriate security or the Trust shall be insured against losses arising out of any such advances; or

(b) a majority of the Disinterested Trustees acting on the matter (provided that a majority of the Disinterested Trustees then in office act on the matter) or independent legal counsel in a written opinion shall determine, based upon a review of the readily available facts (as opposed to a full trial-type inquiry), that there is reason to believe that the recipient ultimately will be found entitled to indemnification.

As used in this Section 4, a “Disinterested Trustee” is one (x) who is not an Interested Person of the Trust (including anyone, as such Disinterested Trustee, who has been exempted from being an Interested Person by any

Part C-6

rule, regulation or order of the Commission), and (y) against whom none of such actions, suits or other proceedings or another action, suit or other proceeding on the same or similar grounds is then or has been pending.

As used in this Section 4, the words “claim,” “action,” “suit” or “proceeding” shall apply to all claims, actions, suits, proceedings (civil, criminal, administrative or other, including appeals), actual or threatened; and the words “liability” and “expenses” shall include without limitation, attorneys’ fees, costs, judgments, amounts paid in settlement, fines, penalties and other liabilities.

The trustees and officers of the Registrant are covered by the Mutual Fund Professional Liability policy in the aggregate amount of $70,000,000 against liability and expenses of claims of wrongful acts arising out of their position with the Registrant and other Nuveen funds, except for matters that involve willful acts, bad faith, gross negligence and willful disregard of duty (i.e., where the insured did not act in good faith for a purpose he or she reasonably believed to be in the best interest of the Registrant or where he or she had reasonable cause to believe this conduct was unlawful). The policy has a $1,000,000 deductible for operational failures and $1,000,000 deductible for all other claims.

The Underwriting Agreement filed or to be filed as an exhibit to this Registration Statement will provide for each of the parties thereto, including the Registrant and the underwriter, to indemnify the others, their trustees, directors, certain of their officers, trustees, directors and persons who control them against certain liabilities in connection with the offering described herein, including liabilities under the federal securities laws.

Insofar as indemnification for liability arising under the Securities Act of 1933, as amended, (the “1933 Act”) may be permitted to directors, officers and controlling persons of the Registrant pursuant to the foregoing provisions, or otherwise, the Registrant has been advised that, in the opinion of the Securities and Exchange Commission, such indemnification is against public policy as expressed in the 1993 Act and is, therefore, unenforceable. In the event that a claim for indemnification against such liabilities (other than the payment by the Registrant of expenses incurred or paid by a director, officer or controlling person of the Registrant in the successful defense of any action, suit or proceeding) is asserted by such director, officer or controlling person in connection with the securities being registered, the Registrant will, unless in the opinion of its counsel the matter has been settled by controlling precedent, submit to a court of appropriate jurisdiction the question whether such indemnification by it is against public policy as expressed in the 1933 Act and will be governed by the final adjudication of such issue.

Nuveen Fund Advisors manages the Registrant and serves as investment adviser or manager to other open-end and closed-end management investment companies and to separately managed accounts. The principal business address for all of these investment companies and the persons named below is 333 West Wacker Drive, Chicago, Illinois 60606.

A description of any other business, profession, vocation or employment of a substantial nature in which the directors and officers of Nuveen Fund Advisors who serve as officers or Trustees of the Registrant have engaged

Nuveen Asset Management LLC (“NAM”) currently serves as sub-adviser to the Fund and as an investment adviser or sub-adviser to certain other open-end and closed-end funds and as investment adviser to separately managed accounts. The address for NAM is 333 West Wacker Drive, Chicago, Illinois 60606. See “Investment Adviser, Sub-Adviser and Portfolio Manager” in Part B of the Registration Statement.

Part C-8

Set forth below is a list of each director and officer of NAM, indicating each business, profession, vocation or employment of a substantial nature in which such person has been, at any time during the past two fiscal years, engaged for his or her own account or in the capacity of director, officer, partner or trustee.

Item 32: Location of Accounts and Records.

Nuveen Fund Advisors, LLC, 333 West Wacker Drive, Chicago, Illinois 60606, maintains the Fund’s Declaration of Trust, By-Laws, minutes of trustee and shareholder meetings, and contracts of the Registrant and all advisory material of the investment adviser. Nuveen Asset Management, LLC, in its capacity as sub-adviser, may also hold certain accounts and records of the Fund.

Computershare Inc., 250 Royall Street, Canton, Massachusetts 02021 maintains all general and subsidiary ledgers, journals, trial balances, records of all portfolio purchases and sales, and all other required records not maintained by Nuveen Fund Advisors or NAM.

Item 33: Management Services.

Not applicable.

Item 34: Undertakings.

1. Not applicable.

2. Not applicable.

Part C-9

3. The Registrant undertakes:

(a) to file, during any period in which offers or sales are being made, a post-effective amendment to this Registration Statement:

(1) to include any prospectus required by Section 10(a)(3) of the Securities Act;

(2) to reflect in the prospectus any facts or events after the effective date of the Registration Statement (or the most recent post-effective amendment thereof) which, individually or in the aggregate, represent a fundamental change in the information set forth in the Registration Statement; and

(3) to include any material information with respect to the plan of distribution not previously disclosed in the Registration Statement or any material change to such information in the Registration Statement.

(b) that, for the purpose of determining any liability under the Securities Act, each post-effective amendment shall be deemed to be a new registration statement relating to the securities offered therein, and the offering of such securities at that time shall be deemed to be the initial bona fide offering thereof;

(c) to remove from registration by means of a post-effective amendment any of the securities being registered which remain unsold at the termination of the offering; and

(d) that, for the purpose of determining liability under the Securities Act to any purchaser:

(1) if the Registrant is relying on Rule 430B:

(A) Each prospectus filed by the Registrant pursuant to Rule 424(b)(3) shall be deemed to be part of the registration statement as of the date the filed prospectus was deemed part of and included in the registration statement; and

(B) Each prospectus required to be filed pursuant to Rule 424(b)(2), (b)(5), or (b)(7) as part of a registration statement in reliance on Rule 430B relating to an offering made pursuant to Rule 415(a)(1)(i), (x), or (xi) under the Securities Act for the purpose of providing the information required by Section 10 (a) of the Securities Act shall be deemed to be part of and included in the registration statement as of the earlier of the date such form of prospectus is first used after effectiveness or the date of the first contract of sale of securities in the offering described in the prospectus. As provided in Rule 430B, for liability purposes of the issuer and any person that is at that date an underwriter, such date shall be deemed to be a new effective date of the registration statement relating to the securities in the registration statement to which that prospectus relates, and the offering of such securities at that time shall be deemed to be the initial bona fide offering thereof. Provided, however, that no statement made in a registration statement or prospectus that is part of the registration statement or made in a document incorporated or deemed incorporated by reference into the registration statement or prospectus that is part of the registration statement will, as to a purchaser with a time of contract of sale prior to such effective date, supersede or modify any statement that was made in the registration statement or prospectus that was part of the registration statement or made in any such document immediately prior to such effective date; or

Part C-10

(2) Not Applicable.

(e) that for the purpose of determining liability of the Registrant under the Securities Act to any purchaser in the initial distribution of securities:

The undersigned Registrant undertakes that in a primary offering of securities of the undersigned Registrant pursuant to this registration statement, regardless of the underwriting method used to sell the securities to the purchaser, if the securities are offered or sold to such purchaser by means of any of the following communications, the undersigned Registrant will be a seller to the purchaser and will be considered to offer or sell such securities to the purchaser:

(1) any preliminary prospectus or prospectus of the undersigned Registrant relating to the offering required to be filed pursuant to Rule 424 under the Securities Act;

(2) free writing prospectus relating to the offering prepared by or on behalf of the undersigned Registrant or used or referred to by the undersigned Registrant;

(3) the portion of any other free writing prospectus or advertisement pursuant to Rule 482 under the Securities Act relating to the offering containing material information about the undersigned Registrant or its securities provided by or on behalf of the undersigned Registrant; and

(4) any other communication that is an offer in the offering made by the undersigned Registrant to the purchaser.

4. Not Applicable.

5. The undersigned Registrant hereby undertakes that, for purposes of determining any liability under the Securities Act, each filing of the Registrant’s annual report pursuant to Section 13(a) or Section 15(d) of the Exchange Act that is incorporated by reference into the registration statement shall be deemed to be a new registration statement relating to the securities offered therein, and the offering of such securities at that time shall be deemed to be the initial bona fide offering thereof.

6. Insofar as indemnification for liabilities arising under the Securities Act may be permitted to directors, officers and controlling persons of the Registrant pursuant to the foregoing provisions, or otherwise, the Registrant has been advised that in the opinion of the Securities and Exchange Commission such indemnification is against public policy as expressed in the Act and is, therefore, unenforceable. In the event that a claim for indemnification against such liabilities (other than the payment by the Registrant of expenses incurred or paid by a director, officer or controlling person of the Registrant in the successful defense of any action, suit or proceeding) is asserted by such director, officer or controlling person in connection with the securities being registered, the Registrant will, unless in the opinion of its counsel the matter has been settled by controlling precedent, submit to a court of appropriate jurisdiction the question whether such indemnification by it is against public policy as expressed in the Act and will be governed by the final adjudication of such issue.

7. The Registrant undertakes to send by first class mail or other means designed to ensure equally prompt delivery, within two business days of receipt of a written or oral request, any prospectus or Statement of Additional Information.

Part C-11

SIGNATURES

Pursuant to the requirements of the Securities Act of 1933 and the Investment Company Act of 1940, the Registrant has duly caused this Registration Statement to be signed on its behalf by the undersigned, thereunto duly authorized, in this City of Chicago, and State of Illinois, on the 19th day of February, 2021.

Pursuant to the requirements of the Securities Act of 1933, this Registration Statement has been signed below by the following persons in the capacities and on the date indicated.

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