NEW YORK — Former Dewey & LeBoeuf chairman Steven Davis has agreed to pay the bankrupt firm’s estate more than $500,000 as part of a broader settlement that is expected to insulate him from most future claims related to his alleged mismanagement of the firm.

Under a deal filed with the bankruptcy court on April 11, Dewey insurer XL Specialty Insurance Co. will contribute $19 million to the estate to help pay off the firm’s creditors.