§ 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.

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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.