I live in the U.S. So that's why it may be different where you live. It also depends on the trainer as well, but typically no one would want you to ride the horse into the ground because granted, they are school horses, and school horses are ridden by a lot of people, they can't afford to be jumped super high by everyone, if you know what I mean. School horses are meant to be ridden by beginners, and as you progress, you begin leasing then owning. If u can't afford a horse, then you probably won't be able to jump very high. That's just the ugly truth I guess. Horsebackriding isn't called the sport of kings for nothing. Especially once u get to the upper levels.
Unfortunately you probably will not get anywhere without your own horse. I don't know much about where you live, but in my area, u basically can't jump over 2 feet on lesson horses. Many of the good places require riders to own a horse or at least lease a horse.
I live in Antigua and I jump approximately .90m and I don’t have a horse . I’d really like to reach new heights and find a good place to train as I can’t really progress to new heights here in Antigua .