At the next regular May election held at least sixty days after the adoption of the consolidation ordinance by the governing bodies or, if applicable, the election at which the consolidation is approved by the voters, such officers as are provided for by general or special law shall be elected for the consolidated city or town. Their terms shall begin on July 1 next succeeding their election, at which time they shall replace all elective city or town officers of the consolidated cities or towns whose terms shall terminate on such day. The terms of the new officers shall expire on January 1 for constitutional officers next succeeding the regular election of city constitutional officers in the Commonwealth and July 1 next succeeding the regular election of all other city and town officers. All appointive city and town officers shall be appointed by the person, board or authority upon whom the power to appoint such officers in other cities and towns is conferred. The terms of such officers shall commence on January 1 next succeeding the first election of officers for the consolidated city or town and shall continue, unless otherwise removed, until their successors have been appointed and qualified. The successors of all such officers whose first election or appointment is herein provided for shall thereafter be elected or appointed at the time, in the manner and for the terms provided by general or special law.