NINTH AMENDMENT TO TAX ASSET PROTECTION PLAN

Exhibit 4.1

NINTH AMENDMENT TO

TAX ASSET PROTECTION PLAN

This NINTH AMENDMENT TO TAX ASSET PROTECTION PLAN (this “Amendment”) is entered into as of April 15, 2026, by and between Arq, Inc. (formerly Advanced Emissions Solutions, Inc.), a Delaware corporation (the “Company”), and Computershare Trust Company, N.A., a federally chartered trust company (the “Rights Agent”). All capitalized terms used herein and not otherwise defined herein shall have the meaning(s) ascribed to them in that certain Tax Asset Protection Plan dated as of May 5, 2017, by and between the Company and the Rights Agent, as amended by the First Amendment to Tax Asset Protection Plan, dated as of April 6, 2018, the Second Amendment to Tax Asset Protection Plan, dated as of April 5, 2019, the Third Amendment to Tax Asset Protection Plan, dated as of April 8, 2020, the Fourth Amendment to Tax Asset Protection Plan, dated as of April 9, 2021, the Fifth Amendment to Tax Asset Protection Plan, dated as of March 15, 2022, the Sixth Amendment to Tax Asset Protection Plan, dated as of April 13, 2023, the Seventh Amendment to Tax Asset Protection Plan, dated as of April 15, 2024, and the Eighth Amendment to Tax Asset Protection Plan, dated as of April 8, 2025 (collectively, the “▇▇▇▇”).

RECITALS

WHEREAS, the Company and the Rights Agent are parties to the TAPP; and

WHEREAS, pursuant to Section 26 of the TAPP, the Company and the Rights Agent desire to amend the ▇▇▇▇ as set forth in this Amendment.

AGREEMENT

NOW, THEREFORE, in consideration of the promises and the mutual agreements herein set forth, the parties hereto hereby agree as follows:

1.Amendment of Section 1(w). The definition of “Final Expiration Date” set forth in Section 1(w) of the ▇▇▇▇ is hereby amended and restated to read in its entirety as follows:

“(w) “Final Expiration Date” shall mean the Close of Business on the earlier of (i) December 31, 2027 or (ii) December 31, 2026 if Stockholder Approval has not been obtained prior to such date.”

2.Amendment of Exhibit B (Form of Rights Certificate). The introductory paragraph of Exhibit B to the ▇▇▇▇ is hereby deleted and replaced with the following:

“NOT EXERCISABLE AFTER THE EARLIER OF (I) DECEMBER 31, 2027 OR (II) DECEMBER 31, 2026 IF STOCKHOLDER APPROVAL HAS NOT BEEN OBTAINED PRIOR TO SUCH DATE, OR SUCH EARLIER DATE AS PROVIDED BY THE TAX ASSET PROTECTION PLAN. THE RIGHTS ARE SUBJECT TO REDEMPTION AND EXCHANGE AT THE OPTION OF THE COMPANY, ON THE TERMS SET FORTH IN THE TAX ASSET PROTECTION PLAN. UNDER CERTAIN CIRCUMSTANCES AS SET FORTH IN THE TAX ASSET PROTECTION PLAN, RIGHTS THAT ARE OR WERE BENEFICIALLY OWNED BY AN ACQUIRING PERSON OR ANY AFFILIATE OR ASSOCIATE OF AN ACQUIRING PERSON (AS SUCH TERMS ARE DEFINED IN THE TAX ASSET PROTECTION PLAN) MAY BECOME NULL AND VOID.”

3.Amendment of Exhibit C (Summary of Rights). Exhibit C to the ▇▇▇▇ is hereby amended in that the section titled “Expiration” is hereby deleted and replaced with the following:

“Expiration. The Rights and the Plan will expire on the earlier of (i) the Close of Business on the earlier of (a) December 31, 2027 or (b) December 31, 2026 if Stockholder Approval has not been obtained prior to such date, (ii) the time at which the Rights are redeemed pursuant to the Plan, (iii) the time at which the Rights are exchanged in full pursuant to the Plan, (iv) the effective date of the repeal of both Section 382 and Section 383 of the Internal Revenue Code, or any successor provisions or replacement provisions, if the Board determines that the Plan is no longer necessary for the preservation of Tax Benefits or (v) the beginning of a taxable year of the Company for which the Board determines that the Company has or will have no Tax Benefits.”

4.Agreement as Amended. The term “Agreement” as used in the TAPP shall be deemed to refer to the ▇▇▇▇ as amended. Except as set forth herein, the ▇▇▇▇ shall remain in full force and effect and otherwise shall be unaffected hereby, and each of the Company and the Rights Agent shall continue to be subject to its terms and conditions.

5.Severability. If any term, provision, covenant or restriction of this Amendment is held by a court of competent jurisdiction or other authority to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Amendment shall remain in full force and effect and shall in no way be affected, impaired or invalidated; provided, however, that if such excluded terms, provisions, covenants or restrictions shall adversely affect the rights, immunities, liabilities, duties, responsibilities or obligations of the Rights Agent, the Rights Agent shall be entitled to resign immediately.

6.Governing Law. This Amendment shall be deemed to be a contract made under the laws of the State of Delaware and for all purposes shall be governed by and construed in accordance with the laws of such State applicable to contracts made and to be performed entirely within such State.

7.Counterparts. This Amendment may be executed in any number of counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument. A facsimile or .pdf signature delivered electronically shall constitute an original signature for all purposes.

8.Descriptive Headings. Descriptive headings of the several Sections of this Amendment are inserted for convenience only and shall not control or affect the meaning or construction of any of the provisions hereof.

[Signature Page Follows]

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    IN WITNESS WHEREOF, each of the parties hereto has caused this Amendment to be duly executed as of the date first above written.

ARQ, INC.

By:

/s/ ▇▇▇▇▇▇ ▇▇▇▇▇▇

Name: ▇▇▇▇▇▇ ▇▇▇▇▇▇

Title: Chief Executive Officer

COMPUTERSHARE TRUST COMPANY, N.A.

By:

/s/ ▇▇▇▇▇▇▇ ▇▇▇▇▇

Name: ▇▇▇▇▇▇▇ ▇▇▇▇▇

Title: Manager, Client Management