New York Laws
Article 34 - Calendar Practice; Trial Preferences
R3403 - Trial Preferences.

(b) Obtaining preference. Unless the court otherwise orders, notice of
a motion for preference shall be served with the note of issue by the
party serving the note of issue, or ten days after such service by any
other party; or thereafter during the pendency of the action upon the
application of a party who reaches the age of seventy years, or who is
terminally ill.