6-K

CAPITAL CLEAN ENERGY CARRIERS CORP.

Dated: August 10, 2026

/s/ Gerasimos (Jerry) Kalogiratos

Name: Gerasimos (Jerry) Kalogiratos

Title: Chief Executive Officer

On August 7, 2026, Capital Clean Energy Carriers Corp. (the “Corporation”) issued a press release announcing an annual meeting of shareholders, which is attached as Exhibit I.

Attached as Exhibit II are a cover letter to the shareholders of the Corporation, formal notice of annual meeting of shareholders and proxy statement, each dated August 7, 2026.

Attached as Exhibit III is the Proxy Card for the 2026 annual meeting of shareholders of the Corporation for holders of its common shares.

Nomination of Ms. Janet DiFiore to the Board of Directors

On August 7, 2026, the Corporation also announced that Mr. Gurpal Grewal has determined not to stand for re-election at the annual meeting of shareholders of the Corporation. To fill the seat vacated by Mr. Gurpal Grewal, Ms. Janet DiFiore has been nominated by the Nominating Committee of the Board of Directors and the Board of Directors for election to serve as Director from the upcoming annual meeting of shareholders until the 2027 annual meeting of shareholders or until a successor is duly elected and qualified or until her earlier death, resignation, disqualification or removal.

Janet DiFiore has 40 years of experience as a prosecutor, trial lawyer, trial judge and appellate judge, and has held senior leadership and executive positions in the public sector for more than 25 years. Ms. DiFiore began her career as an Assistant District Attorney in the Westchester County District Attorney’s Office and later returned to that office as Chief of the Narcotics Bureau. In 1998, she was elected to the Westchester County Court, and in 2002 she was elected a Justice of the New York State Supreme Court for the 9th Judicial District, where she subsequently served as Supervising Judge of the Criminal Courts. In 2005, she was elected District Attorney of Westchester County and was reelected in 2009 and 2013. She has also served as President of the New York State District Attorneys Association and as Chair of the New York State Joint Commission on Public Ethics. On December 1, 2015, Ms. DiFiore was appointed Chief Judge of the New York Court of Appeals and the State of New York and, after unanimous confirmation by the New York State Senate in January 2016, she served in that role until her retirement from government service in 2022. She is a recipient of the Deming Cup awarded by Columbia Business School. Judge DiFiore holds a B.A. from C.W. Post College, Long Island University and a J.D. from St. John’s University School of Law.

The paragraphs under the title “Nomination of Ms. Janet DiFiore to the Board of Directors” in this report on Form 6-K are hereby incorporated by reference into the registrant’s Registration Statement on Form F-3 (File No. 333-282610), Registration Statement on Form F-3 (File No. 333-286825) and Registration Statement on Form F-3 (File No. 333-287895).