If the chair wishes to resign from that role but continue to be a member of the council, section 88 states:-
"On a casual vacancy occurring in the office of chairman of any council, an election to fill the vacancy shall be held not later than the next ordinary meeting of the council held after the date on which the vacancy occurs, or if that meeting is held within fourteen days after that date, then not later than the next following ordinary meeting of the council, and shall be conducted in the same manner as an ordinary election."
In other words, you must have a gap of at least two weeks between the resignation of the chair and the election of a successor. The vice-chair, if you have one, assumes the role in the interim.