N.Y. Civil Practice Law & Rules Law § 7504 (2026)

§ 7504. Court appointment of arbitrator. If the arbitration agreement
does not provide for a method of appointment of an arbitrator, or if the
agreed method fails or for any reason is not followed, or if an
arbitrator fails to act and his successor has not been appointed, the
court, on application of a party, shall appoint an arbitrator.