2006 New York Code - Vacancy, How Filled.

 
    § 182. Vacancy, how filled. When a vacancy shall occur, otherwise than
  by  expiration  of term, in the office of police justice, the same shall
  be filled, for the balance of the  unexpired  term,  at  the  next  city
  election  happening not less than thirty days after such vacancy occurs.
  Until such vacancy shall be so filled, the mayor may appoint a qualified
  attorney to fill the same, who shall hold office until the first day  of
  January after the election at which his successor is elected.