I think Levy will hold firm, while Kane still has years left on his contract, Levy holds power and I think Kane would cost too much money this year.
This contract he signed some years back is silly though. He should have thought to himself, "when I'm 28, if I still haven't won something with Spurs, I need the power to make a quick and easy escape from the club," and negotiate on those principles. This 'gentleman's agreement' is ridiculous, you should never assume that the other party will uphold it as these things can be twisted to suit ones agenda, if Levy really meant it, then he should be made to put it into the contract.
This is the case if Kane has indeed refused to turn up to training and it isn't a case of he should be coming back at a later date.