N.Y. Civil Practice Law & Rules § 5519
(e) Continuation of stay. If the judgment or order appealed from is affirmed or modified, the stay shall continue for five days after service upon the appellant of the order of affirmance or modification with notice of its entry in the court to which the appeal was taken. If an appeal is taken, or a motion is made for permission to appeal, from such an order before the expiration of the five days, the stay shall continue until five days after service of notice of the entry of the order determining such appeal or motion. When a motion for permission to appeal is involved, the stay, or any other stay granted pending determination of the motion for permission to appeal, shall: