THIS AMENDING AGREEMENT made effective as of the 17th day of December, 2025 AMONG:

Exhibit 10.13

THIS AMENDING AGREEMENT made effective as of the 17th day of December, 2025

AMONG:

THE METALS ROYALTY COMPANY INC., (formerly, Low Carbon Royalties Inc.) a corporation duly incorporated under the laws of the Province of British Columbia (the “Corporation”)

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ODYSSEY TRUST COMPANY, a trust company authorized to carry on business in all provinces and territories of Canada (the “Subscription Receipt Agent”)

WHEREAS:

A. The Corporation and the Subscription Receipt Agent entered into a subscription receipt agreement dated as of July 25, 2025 (the “Subscription Receipt Agreement”) pursuant to which, among other things, the Corporation issued 3,134,481 Subscription Receipts exercisable into Underlying Shares in the manner set forth in the Subscription Receipt Agreement;

B. The Subscription Receipt Agent agreed to act as registrar and transfer agent for the Subscription Receipts, and as escrow agent to receive the Escrowed Funds;

C. Pursuant to Section 1.1 (o) of the Subscription Receipt Agreement, the “Escrow Release Deadline” was 5:00 p.m. (Vancouver time) on December 31, 2025;

D. Pursuant to Section 8.10 of the Subscription Receipt Agreement, the Subscription Receiptholders have the power, exercisable by special resolution at a duly convened meeting, to assent to any modification of the provisions contained in the Subscription Receipt Agreement and to authorize the Subscription Receipt Agent to concur in and execute any ancillary or supplemental agreement embodying the change;

E. Pursuant to Section 8.14 of the Subscription Receipt Agreement, all actions and powers that may be taken or exercised by Subscription Receiptholders at a duly convened meeting may also be taken and exercised by an instrument in writing;

F. The Subscription Receiptholders, by an instrument in writing, approved a special resolution to extend the Escrow Release Deadline to 5:00 p.m. (Vancouver time) on March 31, 2026 (the “Extension Resolution”);

G. Pursuant to Section 9.1(b) of the Subscription Receipt Agreement, the Corporation and the Subscription Receipt Agent may execute and deliver agreements supplemental to the Subscription Receipt Agreement, which thereafter shall form part of the Subscription Receipt Agreement, giving effect to any special resolution passed as provided in Article 8 of the Subscription Receipt Agreement;

H. The Corporation wishes to amend the Subscription Receipt Agreement to effect the Extension Resolution; and

I. The foregoing recitals are made as statements of fact by the Corporation and not by the Subscription Receipt Agent.

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NOW THEREFORE THIS AGREEMENT WITNESSES THAT in consideration of the covenants and agreements contained herein and for other good and valuable consideration, the parties hereto agree to amend the Subscription Receipt Agreement as provided herein:

Section 1 General

In this Amending Agreement (including the recitals) unless otherwise defined or the context otherwise requires, all capitalized terms shall have the respective meanings specified in the Subscription Receipt Agreement (including as amended by this Amending Agreement).

Section 2 To be Read with Subscription Receipt Agreement

This Amending Agreement is an amendment to the Subscription Receipt Agreement. Unless the context of this Amending Agreement otherwise requires, the Subscription Receipt Agreement and this Amending Agreement shall be read together and shall have effect as if the provisions of the Subscription Receipt Agreement and this Amending Agreement were contained in one agreement. The term “Agreement” when used in the Subscription Receipt Agreement means the Subscription Receipt Agreement as amended, supplemented or modified from time to time (including as amended by this Amending Agreement).

Section 3 Amendments

Section 1.1 (o) of the Subscription Receipt Agreement is hereby amended by deleting such Section in its entirety and replacing it with the following:

“Escrow Release Deadline” means 5:00 p.m. (Vancouver time) on March 31, 2026;

Section 4 No Other Amendments, Waivers or Consents

(a) Except as expressly amended, waived or consented to herein, the Subscription Receipt Agreement, as well as any document or agreement entered into between the parties in connection thereto shall be unmodified and shall continue to be in full force and effect in accordance with their terms.

(b) The Subscription Receipt Agreement shall be deemed to be amended as of and from the date hereof.

(c) All provisions of the Subscription Receipt Agreement, as amended by this Amending Agreement, are hereby ratified and confirmed and shall continue in full force.

Section 5 Counterparts

This Amending Agreement may be executed in any number of separate counterparts by facsimile, pdf copy or other electronic form, each of which shall be deemed an original and all of said counterparts taken together shall be deemed to constitute one and the same instrument.

Section 6 Severability

If any term or provision of this Amending Agreement or the application thereof to any party or circumstance shall be held to be invalid, illegal or unenforceable in any respect by a court of competent jurisdiction, the validity, legality and enforceability of the remaining terms and provisions of this Amending Agreement shall not in any way be affected or impaired thereby, and the affected term or provision shall be modified to the minimum extent permitted by law so as most fully to achieve the intention of this Amending Agreement.

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Section 7 Governing Law

This Amending Agreement shall be governed by, and construed and enforced in accordance with, the laws of the Province of British Columbia and the laws of Canada applicable therein and shall be treated in all respects as a British Columbia contract.

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IN WITNESS WHEREOF the parties hereto have executed this Amending Agreement.

	THE METALS ROYALTY COMPANY INC.
	Per:	(Signed) “▇▇▇▇▇▇ ▇▇▇▇▇▇”
		Authorized Signing Officer
		ODYSSEY TRUST COMPANY
	Per:	(Signed) “▇▇▇▇▇ ▇▇▇▇▇”
		Authorized Signing Officer
	Per:	(Signed) “▇▇▇▇▇ ▇▇▇▇▇▇▇▇▇”
		Authorized Signing Officer