New York Consolidated Laws, Surrogate's Court Procedure Act - SCP § 706. When surviving or remaining fiduciary may act;  when successor must be appointed

1. Where one of two or more fiduciaries dies or is removed or where letters issued to one of them are revoked, a successor to the deceased fiduciary or to the one who has been removed or whose letters have been revoked shall not be appointed, except where such appointment is necessary in order to comply with the express terms of a will or lifetime trust instrument;  but the others may proceed and complete the administration of the estate pursuant to the letters or lifetime trust instrument and may continue any action or special proceeding brought by or against all.

2. When all the persons to whom letters have been issued die or where letters issued to all of them have been revoked by a decree of the surrogate's court, or, in the case of a lifetime trust, when all persons serving as trustee die or are removed, without any successor trustee having been effectively appointed pursuant to the terms of the lifetime trust instrument, that court has, except in a case where it is otherwise specially prescribed by law, the same power to appoint a successor to the person or persons whose powers have ceased as if the letters had not been issued or as if no appointment had been made.  The successor may complete the administration of the estate committed to his predecessor, he may continue in his own name a civil action or proceeding pending in favor of his predecessor and he may enforce a judgment, order or decree in favor of the latter.