In the event of a change in the method of government heretofore or hereafter adopted in any city in which a pension corporation has been incorporated under this chapter, the corporation shall not thereby become inoperative, but shall extend to and continue in force and effect in so far as the provisions of this chapter may be consistent with such change and rearrangement of the duties and positions of the members of the pension corporation. The provisions hereof shall apply to any new board, body or authority which shall be charged with the supervision of the department or departments under which the members of any such pension corporation are employed.