I would want to know which clematis you are considering. That's a good sized container but most clems develop a very large root system that could pretty much fill that up! I grow a number of clems in containers but individually and most are at least 20G....wider than yours but not as deep.

My concern would be that when the time came to repot and refresh the potting soil, the roots would be hopelessly intermingled. And I am unsure about using a board or whatever to separate......that just bothers me in a container setting.

I have a couple of containers ( 20" by 18") with two clems in them and also containers with roses and clematises. Planted 2 years ago - so far so good. No division between them. I don't plan to repot them for now. Just adding fertilizers. Before planting make sure that your varieties are suitable for container culture and are the same pruning group. I would recommend Raymond Evison's clematises. They are best for containers: shorter and a lot of flower power. Good luck.