After you figure out and rule out that your horse doesn’t have a medical problem. If they rear lean as far forward as you can. If your horse bucks try and pick its head up and just keep moving forward.
Figure out if there’s any pain first. If there’s none ride then toward through the buck and if they rear smack their ears while their up in the air. It makes them think they’ve hit a roof and they stop rearing. I’ve never had a horse rear more than twice on me with this method
If you can’t get the buck under control, try turning your horse into a circle so it disengages their hind end so it’s harder to buck.
If she bucks sit up tall and ride her forward threw them and keep your hands soft and low don’t let them pop up or pull on her mouth this will only upset her more. Keeping her head up too much will make her want to rear and that can be much more dangerous then bucking if she rears again keep your hands low and go with her dot let your weight fall back this could cause her to fall back. Also check out with the vet why she is doing this it could be she is in pain. If she just starts out like this and works out of it try putting her on a lounge line and letting her get her jumps out before you get on.
My motto has always been that "punishment" for bad behavior comes in the form of working harder. So if and when my horse does that I make her canter pretty hard in a tight circle for a couple minutes. It requires lots of work on her end. Eventually she stopped because she's knows it's not worth having to do extra work. That doesn't work for every horse though, just a thought. Also, rule out other options first like possible pain anywhere or something wrong that your horse is trying to tell you.
Push them forward!! I know it is probably the hardest thing to do when the horse you’re sitting on is jumping up and down and kicking out, trust me I know lol! But push them forward because you need to tell them that they can buck and kick and be naughty but they still have to do the work and you aren’t going anywhere!