Whenever the office of a member of Council shall become vacant, the vacancy shall be filled by a majority vote of all the remaining members of the Council. If the vacancy shall not be so filled within thirty (30) days, the Mayor shall fill it by appointment. A member of Council elected or appointed to fill a vacancy shall hold office for the balance of the unexpired term or until a successor shall be elected and shall qualify for the unexpired term as hereinafter provided. A successor shall be elected for the unexpired term to fill any such vacancy at the next regular Municipal or general election.