Indeed, your clematis does, as Hollie-Hock says, need a very much larger pot - but not now while it is flowering. I grow several clematis in pots, usually about 15 inches across and up to 18 inches deep - less than that and the roots can get warm, which they hate. A deep root run, cool soil and warm heads make happy clematis. Plenty of feed, clems are hungry plants, prune as and when - depending on the type of clematis. Some of the alpinas make stunning pot plants, there are large flowered hybrids especially bred to keep shortish for pots, and if there is something deent to climb then the vitcellas are great. I don't subject big flowered summer ones to pots any more, though I am of the persuasion that you can grow anything in a pot - mostly I think because I no longer grow large flowered summer hybrids - they are just too delicate and sensitive for the garden here, the tough and pretty small ones work better. We have some of the non-climbing ones too, which are lovely, not particularly floriferous yet, but so unexpected creeping over a box shrub or beside a stately old phormium - or just tumbling about where they feel like it as I have forgotten where I planted them.