Preventing ModelBuilder model from working on/after particular date?

I have not tested this but you could try using an if statement in a Calculate Value tool to issue a sys.exit() if today's date is greater than the date you want your model to cease working.

Then make that tool element a precondition to the rest of your model running.

Alternatively, as commented by @BERA:

You could rename or delete the Toolbox (*.tbx file) using a script in the operating system which executes at the desired date.