Fold pre. As played, you can't shove. Villain could easily play the naked Ac like this. I disagree that he would stop to think about it OTT necessarily, snap check is very common when people make the nuts (or near nuts here, whatever).
Preflop is a mistake and where you are really losing most of your money in this hand.
As played, check turn. With a good live read you could make a case for betting again but without one there is no way to know if villain is trapping, calling down or ready to fold. With four clubs on the board you mostly are now trying to get to a cheap river. You probably beat more hands then not but not much better is folding and not much worse is calling.
A shove on the turn is awful on many levels. Worse hands are not calling and better hands are going to call. Maybe you can get a T high flush to fold, but I doubt it.
V snap calls 165 on a suited flop, what's he folding to on the turn? I think the snap check is more likely a nutted type hand than it is fear. Unless it's the fear that the 4th club killed his action. Fold.