I'm wondering if any place (city, country, etc.) has planned the end of the use of ICE vehicle - for professional and/or personal use - in a legally binding way (i.e. not just a vague promise but something that will take effect if not otherwise stopped).
According to the Wikipdia article "Mackinac Island On Mackinac Island (Michigan):
Motorized vehicles have been prohibited on the island since 1898, with the exception of city emergency vehicles (ambulance, police cars and fire trucks), city service vehicles and snowmobiles during winter.
I think several other small resort areas in North America, and perhaps elsewhere, have similar restrictions in place.
https://en.wikipedia.org/wiki/Category:Car-free_zones_in_the_United_States lists 18 "car-free zones" but not all of the pages contain good sources for this.
Zermatt, a ski resort town in Switzerland, bans ICE vehicles, but allows businesses to have electric vehicles. See This town banned cars (except tiny electric ones) by Tom Scott.
Tresco is a car-free island. Electric vehicles are used to transport overnight visitors to and from Tresco Heliport and from the various quays, and a few golf carts are available for disabled visitors.
Tresco is 297 hectares in size with a population of around 175 (in 2011) and is administered for the Crown by the Duchy of Cornwall. It is leased to the Dorrien-Smith estate, which runs it as a timeshare business. The Dorrien-Smith family held the position of Lord Proprietors of the Scilly Islands between 1834 and 1920. I believe the ban has been in place for many years and was not originally due to climate change.