What about going backwards like George Pacuilo? Previous NSW MLA now Mayor of Liverpool?

Windermere MLC Ivan Dean was an alderman on Launceston City Council, and
then was elected Mayor of Launceston after being elected to the Legislative

(and doubtless many other similar cases)

It is not allowed for people to be simultaneously mayor of a city and a
member of the Tasmanian House of Assembly.

Peter Macdonald doing it the other way around (he’s Mayor at Manly now) & David Barr who went the usual route in the same seat.

Ivan Petch: State member for Gladecville, defeated in 1995 by John Watkins, later became mayor of the city of Ryde.

Wayne Philips (former MLA from Eltham in the Victorian parliament) was on the Diamond Valley Shire Council in the 1980s / 1990s (including a stint as mayor) and has recently returned as Mayor of Banyule City Council.