The former adult-movie star who accepted $130,000 from President Donald Trump’s lawyer would return the money in exchange for being released from a contract barring her from discussing an alleged sexual encounter with Mr. Trump, according to a letter from her attorney.

The letter Monday to Trump attorney Michael Cohen said Stephanie Clifford, the former actress, would pay Mr. Trump the money by Friday if he and Mr. Cohen agree to end the contract, halt an arbitration proceeding against her and allow Ms. Clifford to speak “openly...