(a) Any party claiming a preference under CPLR 3403 may apply to the court by making a motion in a motion part, in accordance with CPLR 3403(b), the note of issue therein referred to being deemed a preference to a notice of trial.

A counterclaim or cross-claim which is not entitled to a preference shall not itself defeat the plaintiff's right to a preference under this section.

If a preference is granted, the action shall be placed on a ready calendar for a day certain ahead of all nonpreferred pending cases, as directed by the court, unless the court otherwise orders.