Section 4. Commencement of term of office

1.  The term of office of an
  elective officer, unless elected to fill a vacancy then existing,  shall
  commence  on  the  first  day of January next after his election, if the
  commencement thereof be not otherwise fixed by law.
    2. All terms of city officers, including supervisors, elected  in  any
  city  or part of a city, and of county officers in the city of New York,
  shall expire at the end of an odd-numbered year. Such officers shall  be
  elected,   except  to  fill  a  vacancy,  at  the  general  election  in
  odd-numbered years.  This subdivision shall not apply  to  any  judicial
  officer.