Instead of providing for the appointment of the following officers as provided in Section 3.1-30-5, the city council, in its discretion, may provide by ordinance passed by a two-thirds vote of all the alderpersons elected for the election by the electors of the city of a city collector, a city marshal, a city superintendent of streets, a corporation counsel, a city comptroller, or any of them, and any other officers which the city council considers necessary or expedient. By ordinance or resolution, to take effect at the end of the current fiscal year, the city council, by a like vote, may discontinue any office so created and devolve the duties of that office on any other city officer. After discontinuance of an office, no officer filling that office before its discontinuance shall have any claim against the city for salary alleged to accrue after the date of discontinuance.