At first glance, I wondered how stable those are in the wind, but if they are filled with dirt, probably very stable. If you go up higher, you'll add more wind area and raise the overturning forces, but that dirt is probably so heavy it won't matter. I'll mention it anyway in case it is not as stable as I think it is.
I've put in posts and put cattle panels across them for a large permanent trellis. I'm trying one for hops this year and one for scarlet runner beans, trying to shade a small building. I've also set wooden fence posts in my garden and put up fencing as a trellis for pole beans and tomatoes. One mistake I made for the tomatoes was using 2" x 4" plastic coated welded wire fencing. It seemed that half my black krim, which makes a huge tomato, tried to grow inside those 2" x 4" openings. The other large tomatoes behaved a lot better, but not the black krim. If you are using this for tomatoes, use fencing with bigger openings.
I don't think my specific method will work for you, but maybe some variation. I don't know how tall you want to go or how permanent you want to make it. I'll assume not permanent. Maybe use 2" x 4"'s as posts at the end of your planter, set it in the ground pretty shallow to take the weight and anchored maybe with big rock so it cannot move sideways, then fasten it to the ends of your planter which should stabilize it. You can run wire, either a welded wire or single strands of wire, maybe a lattice, maybe string, even 1" x 2" strips of wood, between these "posts" for your plants to climb on.
There will be two different directions of force acting on this. Both will try to rotate your uprights and knock them over. One is the wind hitting your trellis. It will try to rotate your uprights around your top support to the planter. The best way to counter that is to anchor the bottom of your uprights at ground level so they cannot move. The other force is the weight of your plants on the trellis if your trellis is not rigid. If your trellis can bend, and it will probably be able to, the wind will add to this force. Your uprights will try to bend in toward the center of your planter. You can counter this a couple of ways. One is to anchor your uprights at the top of the ground so they cannot move in line with your planter. Maybe big rocks, maybe run a wire or a 2" x 4" under your planter and connect the bottoms of your uprights so they cannot separate. Another way is to put a rigid support at the top of your uprights so they cannot move toward each other, maybe a 2x4?
If the uprights break from the side wind, it will probably be at the top connection to the planter. If they break due to the weight of the plants on the trellis plus wind, it would most likely be at the top of the planter. I'm mentioning this because if you use 2x4 uprights, watch how bad the knots are and where they go. This post is long enough. I'll not tell you how I know knots can seriously weaken a 2x4. It was just a little bump!
I know I've probably gone into a lot more detail than I need to for you. If you are keeping those covers on, there will probably be no effective wind on the trellis. Maybe you don't have that much wind anyway. Depending on what your are growing, maybe you could just stick tree limbs in your planter and let stuff climb that if there is no wind on it. Maybe put 2x4s inside your planter at the ends, with the bottom of the 2x4's pushed down into your planter and fastened at the top to your planter, then stretch wire across. A simple way to fasten them at the top may be to use wire around what looks like our 2x4 top.
I doubt you will do anything exactly as I said, but maybe it will give you some ideas. You usually have a pretty good imagination.
Good luck!!
