It depends on which climber you want to grow.

Question's too general to answer properly, but as a general rule, always choose a smaller climber, something that gets up to 10 feet in the ground. I know from experience that Clematis The President grown in a pot 18 inches high and 12 inches wide will (if kept properly watered) grow to about 4 feet high and slightly less wide, not including the height of the pot.

It also depends on the roots size. A Clematis can have very tangled roots, and doesnt like them being disturbed.