Documents marked “HIGHLY CONFIDENTIAL PROCEEDING” for the first time tie President Donald Trump’s flagship holding company to the continuing effort to silence a former adult-film actress who says she had an affair with Mr. Trump.

A Trump Organization lawyer, Jill A. Martin, is listed as counsel in an arbitration demand for Essential Consultants LLC, a Delaware company formed by Mr. Trump’s personal lawyer and used to pay $130,000 to Stephanie Clifford in exchange for her silence, according to Feb. 22 arbitration documents.