N.Y. Comp. Codes R. & Regs. tit. 22 § 500.25
A request for emergency relief pending the determination of an appeal or a motion for permission to appeal shall be brought on by order to show cause. The applicant shall contact the clerk's office in advance of the filing. The papers shall be filed as directed by the clerk's office. The order to show cause shall include telephone and facsimile numbers for each attorney and self-represented party, and a statement giving reasons for granting the request. If there is no pending appeal or motion for permission to appeal, the order to show cause shall bring on a motion for leave to appeal or be accompanied by a notice of appeal or a motion for permission to appeal complying with section 500.22 of this Part. There is no fee for filing an order to show cause. If a judge signs an order to show cause bringing on a motion, movant shall pay the fee, if any, required by section 500.3(b) of this Part.
N.Y. Comp. Codes R. & Regs. Tit. 22 § 500.25