I don't feel a lot of anxiety before shows, but I sometimes feel it. I have the chance to have many years of experience, so I try to reassure myself by telling me that I already did it so there's no reason I would fail now.
In my mind, I'm telling myself that stress is negative, so I have to get it out of my mind, it sounds silly but it works!
But on the other hand, I ride better when I'm quite stressed. The bigger the show is, the better I ride!
Then, preparation and training are essential, you have to tell yourself that if you worked well before the show, that you couldn't have done better, it helps. There's also a part of luck that you have to accept.
Horses who rushes before fences are horses who try to avoid the rider's hand, either the current hand is too hard, or the previous hand was too hard. Hands stop the horses from handling their jump well, because the contact between the hands and the mouth is direct, and the mouth is very sensitive. If the horse know that he's going to be hurt when he jumps, he'll try to flee.
Most riders with hot horses try to hold them far from the fence, but it'll get worse.
You have to let them free with their neck, while trying to stop them from rushing too much in the last strides.
It's a long work, and it can be complicated for a non-professional rider. You have to be trained and helped. You have to don't be afraid of telling yourself that the more you'll canter, the less your horse will rush.
You can also work on a circle, but you have to be helped by someone who's going to tell you if you have too much hand or not. First, you have to do flat work, you horse have to be able to canter without you holding him.