The election of the Saint Regis tribe of Indians shall be held annually on the first Saturday in June. At each election there shall be elected by a plurality of the votes cast by the qualified voters of such tribe, one chief and one subchief thereto, each of whom shall hold office for a term of three years. At each third annual election dating from that held in the year eighteen hundred and ninety-eight, there shall be elected by a plurality of the votes cast by the qualified voters of said tribe, a clerk, who shall hold office for a term of three years. A successor to such clerk shall be elected at the annual election occuring next prior to the expiration of his term of office. The terms of office of all officers of the Saint Regis tribe shall commence at twelve o’clock noon on the first day of July succeeding the election at which they are elected.