N.Y. Comp. Codes R. & Regs. tit. 22, § 125.1 – Engagement of counsel.

(a) Engagement of counsel shall be a ground for adjournment of an action or proceeding in accordance with this rule.
(b) Engagement of counsel shall mean actual engagement on trial or in argument before any State or Federal trial or appellate court, or in a proceeding conducted pursuant to rule 3405 of the CPLR and the rules promulgated thereunder.
(c) Subject to the provisions of subdivision (f) of this section, where an attorney has conflicting engagements in the same court or different courts, the affected courts shall determine in which matters adjournments shall be granted and in which matters the parties shall proceed. In making such decisions, they shall, to the extent lawful and practicable, give priority to actions and proceedings in the order in which matters are listed below:
1. (1) child protective proceedings;
2. (2) criminal proceedings or juvenile delinquency proceedings wherein the defendant or respondent is incarcerated;
3. (3) proceedings based on acts which constitute felonies;
4. (4) proceedings based on acts which constitute misdemeanors;
5. (5) matrimonial actions and proceedings; and
6. (6) civil actions and proceedings, including proceedings conducted pursuant to rule 3405 of the CPLR and the rules promulgated thereunder. Where an attorney's conflicting engagements include two or more engagements within any one of these categories of actions and proceedings, as between those engagements the affected courts shall give priority to those involving jury trials.
(d) Subject to the provisions of subdivisions (c) and (f) of this section, where an attorney has conflicting engagements, such attorney must proceed in whichever matter is entitled to a statutory preference or, if there is none and none of his or her engagements involves exceptional circumstances, in the particular matter first scheduled for the date on which the conflict arises. Matters involving exceptional circumstances shall be given priority over all others, except those entitled to statutory preference. A court may find exceptional circumstances where: (1) there are four or more attorneys engaged for a trial, hearing or appellate argument therein; (2) a party or material witness will be available for a trial or hearing therein only on the date on which the conflict arises or on any subsequent date during the period such trial or hearing reasonably can be expected to extend; (3) a party or material witness thereto is afflicted with an illness which, because of its nature, requires that the trial of the action or proceeding be held on the date on which the conflict arises; or (4) a trial therein must be conducted within statutory time limits and, if trial of the matter is not held on the date on which the conflict arises, there is a reasonable probability that the time limit applicable thereto will elapse.
1. (1) Each engagement shall be proved by affidavit or affirmation, filed with the court together with proof of service on all parties, setting forth:
  1. (i) the title of the action or proceeding in which counsel is engaged;
  2. (ii) its general nature;
  3. (iii) the court and part in which it is scheduled or, if it is a proceeding conducted pursuant to rule 3405 of the CPLR, the court in which the underlying action was commenced;
  4. (iv) the name of the judge or panel chairman who will preside over it; and
  5. (v) the date and time the engagement is to commence, or did commence, and the date and time of its probable conclusion.
2. (2) In determining an application for adjournment on the ground of engagement elsewhere, the court shall consider the affidavit of engagement and may make such further inquiry as it deems necessary, including:
  1. (i) the dates on which each of the actions or proceedings involved were scheduled for the date on which they conflict;
  2. (ii) whether or not the actions or proceedings involved were marked peremptorily for trial or were the subject of some other special marking;
  3. (iii) the number of times each of the actions or proceedings involved was previously adjourned, and upon whose application;
  4. (iv) if any of the attorneys representing a party to one of the actions or proceedings involved is a member or associate of a law firm or office employing more than one attorney, the number of members or associates of his or her firm or office also serving as cocounsel or otherwise involved in such action or proceeding, and their respective engagements elsewhere; and
  5. (v) if applicable, the period of time each of the actions or proceedings involved has been on a calendar from which it has been called.
(e)
(f) Where a trial already has commenced, and an attorney for one of the parties has an engagement elsewhere, there shall be no adjournment of the ongoing trial except in the sole discretion of the judge presiding thereat; provided that the judge presiding shall grant a reasonable adjournment where the engagement is in an appellate court.
(g) This subdivision shall apply where a date for trial of action or proceeding is fixed at least two months in advance thereof upon the consent of all attorneys or by the court. In such event, the attorneys previously designated as trial counsel must appear for trial on that date. If any of such attorneys is actually engaged on trial elsewhere, he or she must produce substitute trial counsel. If neither trial counsel nor substitute trial counsel is ready to try the case on the scheduled date, the court may impose any sanctions permitted by law.