Mine self supports, and is 8' tall. I frequently tip it to keep the plant bushy and to increase flowering, and simply remove any of the wimpy ground-scrambling branches to the base and prune back wimpy branches to hard growth if they get too long. When it comes time to replace the fence, Tecomas can take a hard prune to make room (It appears from your photo that they are planted a sufficient distance from the fence to do that.) The plant will bounce back.

The picture isn't of the OP's plant. It's a stock picture from the web.

@gyr_falcon That is a stock photo, not my situation. So your advice is to just let is grow like a hedge, scrambling in the general direction you want it to grow?

I can't imagine this rampant plant being kind enough to be 'trained' into doing anything. Huge shrub... very green... but huge if not beaten back.

@CA Kate z9 Left alone it does appear to become a hedge. I wish I had used that as a hedge plant instead of Photinia. But there are also photos online showing Cape Honeysuckle growing on a chain link fence, and then being trimmed tightly to that structure.

If left alone, the plant will take on a large loose mounding habit. Sometimes very long branches that, when they bend over enough to touch the ground, root and then keep going. When removing some from a previous yard, one viney branch was over 30' long, and had resulted in four 4-5' rooted shrubs along the length.

If you want your plants to be more upright and have less a bent on sending out adventure growth, hard pruning as they mature is the best way to make it happen. It blooms on the branch tips, so pruning will encourage the plant produce more flowers, too.

It is a pretty, easy-to-grow and versatile plant. But if you plant it and just let it go, after a while, you may not be able to see enough of your old fence to know when it needs replacing. ;-)

@gyr would this plant do well in clay loam soil, or does it prefer to be in a raised bed with a well-drained soil?

I had one growing along a fence and it got to be 8 - 10 feet tall and the branches rooted where they touched the ground. I eventually took it out because it was to hard to manage and the bottom part didn't get enough sun, so all the leaves and flowers were on the top part of the plant. It grew in ordinary clay soil with very little irrigation.