Any vacancy in the membership of the authority shall be filled by a new member who shall be elected by the remaining members of the authority and who shall serve until the next meeting of the election committee. At the first meeting of the election committee following the filling of such vacancy, the election committee shall elect a member to fill the remainder, if any, of the unexpired term for which such vacancy was filled. Upon such election by the election committee, the membership on the authority of the member previously elected by the remaining members of the authority to fill such vacancy shall terminate.