6-K

UNITED STATES SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER

PURSUANT TO RULE 13a-16 OR 15d-16 UNDER

THE SECURITIES EXCHANGE ACT OF 1934

For the month of September, 2023

Commission File Number: 001-40709

Ardagh MetalPackaging S.A.

(Name of Registrant)

56, rue Charles Martel

L-2134 Luxembourg, Luxembourg

+352 26 25 85 55

(Address of Principal Executive Offices)

Indicate by check mark whether the registrant files or will file annual reports under cover of Form 20-F or Form 40-F.

Form 20-F  x        Form 40-F  ¨

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(1): ¨

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(7): ¨

INFORMATION CONTAINED IN THIS REPORT ON FORM 6-K

This report on Form 6-K comprises of Ardagh Metal Packaging S.A.’s (the “Company”) press release, which is attached hereto as Exhibit 99.1.

Incorporation by Reference

The information set forth in this report on Form 6-K shall be deemed to be incorporated by reference into the registration statement filed on Form F-3, as amended (Registration No. 333-258749) by the Company (including any prospectus forming a part of such registration statement), and to be a part thereof from the date on which this report is furnished, to the extent not superseded by documents or reports subsequently filed or furnished.

EXHIBIT INDEX

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, Ardagh Metal Packaging S.A. has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Date:    September 12, 2023

Exhibit 99.1

Paul Coulson to transition from Chairman toDirector role

Herman Troskie to take up Chairmanship rolein November 2023

Ardagh Metal Packaging S.A. (“Ardagh Metal Packaging”), a leading global supplier of sustainable, infinitely recyclable metal packaging today announces a decision by Paul Coulson to step down as Chairman of Ardagh Metal Packaging, on November 15, 2023.

Mr Coulson will be succeeded by Herman Troskie who currently serves as a director of Ardagh Metal Packaging. Mr Troskie will also succeed Mr Coulson as Chairman of Ardagh Group S.A. (“Ardagh Group”) and ARD Holdings S.A. (“ARD Holdings”), the indirect parent and ultimate parent of Ardagh Metal Packaging, respectively.

This transition is the culmination of a succession process that, in recent years, has seen the appointments of Oliver Graham as CEO of Ardagh Metal Packaging, and Michael Dick as CEO of Ardagh Glass Packaging.

Mr Coulson (71) has been Chairman of Ardagh Group since 1998, leading its development from a single-plant glass operation in Dublin with annual revenue of approximately $50 million, to a global player in sustainable glass and metal packaging, operating across Europe, the Americas and Africa, with annualised revenues of more than $9 billion. Mr Coulson will remain a Director of Ardagh Metal Packaging, Ardagh Group and ARD Holdings, and will remain the controlling shareholder of ARD Holdings.

Herman Troskie (53), a director of Ardagh Metal Packaging, Ardagh Group and ARD Holdings, will succeed Paul Coulson as Chairman of all three companies and will join Ardagh on a full-time basis in November. Based in Luxembourg, Mr Troskie will step down from his current role as CEO of Corporate, Legal and Tax Advisory at Stonehage Fleming, an international family office. He has been a director of Ardagh Group since 2009 and has been closely involved with the growth and development of the Group since then.

About Ardagh Metal Packaging

Ardagh Metal Packaging (AMP) is a leading global supplier of infinitely recyclable, sustainable, metal beverage cans and ends to brand owners. A subsidiary of sustainable packaging business Ardagh Group, AMP is a leading industry player across Europe and the Americas with innovative production capabilities. AMP operates 24 production facilities in nine countries, employing more than 6,300 employees and had sales of $4.7 billion in 2022.

Paul Coulson

Paul Coulson (71) graduated from Trinity College Dublin in 1973 and spent five years with Price Waterhouse in London and Dublin, before establishing his own accounting firm. In 1980, he set up Yeoman International and developed it into a significant leasing and structured finance business. In 1998 he became Chairman of Ardagh and initiated the transformation of the business from a small, single plant glass operation into a leading global packaging company. Over the last 40 years he has been involved in the creation and development of a number of other businesses, including Fanad Fisheries, a leading Irish salmon farming company, and Sterile Technologies which, prior to its sale in 2006, had been developed into the leading medical waste management company in the United Kingdom and Ireland.

Herman Troskie

Herman Troskie (53) is currently the CEO of Corporate, Legal and Tax Advisory at Stonehage Fleming, an international family office. He has extensive experience in the areas of international corporate structuring, cross-border financing and capital markets, with a particular interest in integrated structuring for entrepreneurs and their businesses. He has been a director of Ardagh Group since 2009 and is intimately familiar with the growth and development of the Group over many years. Mr Troskie is also a director of companies within the Yeoman group of companies, and other private and public companies. He qualified as a South African Attorney in 1997, and as a Solicitor of the Senior Courts of England and Wales in 2001.

Forward-Looking Statements

This press release includes “forward-lookingstatements” within the meaning of Section 27A of the U.S. Securities Act and Section 21E of the U.S. Securities ExchangeAct of 1934, as amended. Forward-looking statements are subject to known and unknown risks and uncertainties, many of which may be beyondour control. We caution you that the forward-looking information presented in this press release is not a guarantee of future events,and that actual events may differ materially from those made in or suggested by the forward-looking information contained in this pressrelease. Any forward-looking information presented herein is made only as of the date of this press release, and we do not undertakeany obligation to update or revise any forward-looking information to reflect changes in assumptions, the occurrence of unanticipatedevents, or otherwise. This press release contains inside information for the purposes of Article 7 of Regulation (EU) No 596/2014.The person responsible for the release of this information on behalf of Ardagh Metal Packaging Finance plc and Ardagh Metal PackagingFinance USA LLC is Stephen Lyons, Investor Relations Director.

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