CO open, I 3bet and then we get into awkward flop spot. I literally had no idea of sensible line. I kind of want to just check-fold as I think of this.
SPR of 4 I doubt stacking off is sensible and there is pretty much no good turns. Well we can perhaps assume better made hands would often raise versus cbet so if he call and turn is blank, shoving will be option. But only non club 2-5 are blank so... Well 7 or T would decently often be good.
I would pot and get it in. You are blocking his 2pair+ hands and got even one club blocker.
Ok I bet like 1.6, villain called and turn was 8s. Even if I pot and villain call there will be very often something completing and still have pot behind. So are we not going to be on awkward spot in lot of turns in this case? Are we shoving some non blank turns that complete straight for example? Outside A.
Pot flop, so you can shove turn if you choose to.
I would happily shove anything between 2-8 or pairing card (non-club) and of course any A. J and 9 are the worse, as they complete OESD. 8 and Q are not horrible, as to hit them opponent would need either a gutshot or a wrap.
Agree with Kyyberi.
On this texture we have 2 sizings either pot or small. Be inclined to bet pot with a merged hand like the one you have. Frequency should be like 75%, we smash that board much better with our 3bet-range than villain does.
Watch out for bdfd, draw-blocker or pair-blocker (like you have) to find additional reasons to pot it. Turn is a pot 2barrel unless it brings a :9x:, 
or :club:.
