If a majority of the qualified voters at such election shall vote in favor of the establishment, construction, operation and maintenance of a municipal hospital, the council of the city or town shall elect a board of trustees of such hospital, consisting of three members, one of whom shall be elected for a term of three years, another for a term of two years and the other for a term of one year. Thereafter each member’s successor shall be elected by the council for a term of three years. In the event of a vacancy by death, resignation or change of residence by any trustee from the limits of the city, the council shall immediately elect a trustee to fill the unexpired term.