N.Y. Fam. Ct. Act § 473

§ 473. Substitution of surety. The court may at any time thereafter,\nbefore or after there has been a default, if all arrears have been paid\nin case there shall have been a default on such undertaking, accept a\nnew undertaking in lieu of the original undertaking, and the court shall\nenter an order discharging such undertaking.\n