I don't quite understand the problem that you're describing. Does it happen periodically, or does it only happen when you pedal hard? When you say that it clicks, does it feel like the chain physically slips, or is it just a noise? I also don't understand which bearing surface the "play" is on: the cogs, in between each link, the front chainrings?
If you really wanted to adjust chain tension, which you probably don't, the way to adjust it is by adding or removing links or playing with the adjuster screw, if any, on the derailler.
One way to find and fix these sorts of problems is just to swap components until it goes away. Eg, try a new chain, a different cassette, etc.