N.Y. Real Prop. Acts. Law § 1064
An appeal from a final judgment awarding to the plaintiff possession of the part admeasured and laid off to her does not stay the execution thereof unless the court, or a judge thereof, grants an order directing such a stay. Such an order shall not be granted if an undertaking is given on the part of the respondent, with one or more sureties approved by the court, or a judge thereof, to the effect that, if the judgment appealed from is reversed or modified, and restitution is awarded, she will pay to the person entitled thereto the value of the use and occupation of the part so admeasured and laid off to her, or of the portion restitution of which is awarded, during the time she holds possession thereof, by virtue of the judgment.
N.Y. Real Prop. Acts. Law § 1064