Depends on the fish you plan to add, how big the clarkii are and if they have an anemone.
I never had much problems with clarkii, even had some baby percula with them. But there was no anemone in the tank at that time, so nothing for clowns to fight over.
All clowns will chase away fish that like to pick on anemones - that's kind of a self defense reflex to them.
Usually they ignore all other fish as long as they don't crowd them.
Fish small enough to fit into their mouth may be taken as food, especially if added later.
I had a full grown pair with a juvenile in a green BTA together with 3 Calloplesiops altivelis (Marine Betta), a pair of Chelmon rostratus (Copper Band Buttefly) and a pair of Pseudochellinus hexataenia (Sixline Wrasse) and only the Chelmon and the hexatenia got chased away when the came to close to the anemone and the clarkii's nest. But if they stayed away they were ignored.