Help Me Find states that its height can reach up to 6'7". You might want to use an obelisk support structure and let this rose grow around it.

https://www.helpmefind.com/rose/l.php?l=21.426542

I never believe HMF size estimates. In Joe's zone 9A, I'd think the estimates would be way off. Diane

If you have space for a large bush you can let it grow unsupported. I grow several climbers this way and they go up to 6 or 7 feet tall and then cascade down like a big octopus.

Kiss Me Kate is very stiff and upright for me. I have it planted by an old door and I never even have to fasten it to the door. Big thick stiff canes that only gently curve at the tips when it blooms.

What may cause problems if you try to keep it in a particular size by pruning is that climbers are more likely than other roses to bloom on the ends of canes. That means if you keep pruning the long canes, you'll also prune off most of the blooms. Not a hard and fast rule, but something to consider for climbers. If you let it sprawl to its heart's content that's not an issue, but as other posters have said in zone 9 that's liable to be a big sprawl.

Cynthia