N.Y. Real Property Actions & Proceedings Law § 1064

§ 1064. Appeal not to stay execution if undertaking is given. An\nappeal from a final judgment awarding to the plaintiff possession of the\npart admeasured and laid off to her does not stay the execution thereof\nunless the court, or a judge thereof, grants an order directing such a\nstay. Such an order shall not be granted if an undertaking is given on\nthe part of the respondent, with one or more sureties approved by the\ncourt, or a judge thereof, to the effect that, if the judgment appealed\nfrom is reversed or modified, and restitution is awarded, she will pay\nto the person entitled thereto the value of the use and occupation of\nthe part so admeasured and laid off to her, or of the portion\nrestitution of which is awarded, during the time she holds possession\nthereof, by virtue of the judgment.\n