New York Consolidated Laws, Civil Practice Law and Rules - CVP § 7805. Stay

On the motion of any party or on its own initiative, the court may stay further proceedings, or the enforcement of any determination under review, upon terms including notice, security and payment of costs, except that the enforcement of an order or judgment granted by the appellate division in a proceeding under this article may be stayed only by order of the appellate division or the court of appeals.  Unless otherwise ordered, security given on a stay is effective in favor of a person subsequently joined as a party under section 7802.