This is a critique of the rider as requested only. The setting is schooling and not a show.
The Leg - this rider appears to be pinching at the knee instead of riding with her weight in her heels. The leg has fallen back behind the girth and they have lost upper body balance. Either they were simply left behind on departure due to the inability of the weak leg or fell back into the saddle over the fence.. Either way, this rider is really in the way of the horse by being in the saddle over a fence. Though her heel is below her hip, the amount of bend in the knee and the lack of rising her weight out of the saddle, shows a weak leg a la knee pinching.
Hands - I'm not seeing a release here. It appears as if the rider was trying to balance off the rein and pull herself up into two point, using the reins. This simply jabs the horse in the mouth. Even if you get left behind at a jump, it is best to at least have enough independence in your hands to move them along with your horses' mouth. Impeding the horse with your weight on his back is hard enough but if you also are hanging off his mouth, depending on what bit is in there, your doing everything wrong. Grab mane if need be!
Eye - this rider appears to be looking at the back of her horses' head and not up to where she really wants to go. Her chin is tucked, her eye is down and her shoulders are rotated forward. Keep the eye up beyond your present jump and it will help to keep the shoulders and back in check also.
I don't want to go on and on over this rider's faults. I see many faults but it looks as though she is a novice so as not to discourage her too much, I just stuck with the basic aids. I did not include seat as I don't think this rider has much independence or experience.
I would suggest this rider doing a lot more ground work. Jumping is fun especially if you have a mount that just goes on about it regardless of what you do. But you can also end up discouraging a horse from jumping with so many faults. You can cause a loss of confidence in your horse also depending on his personality. Some horses take faults personally and this can greatly hinder what used to be a packer over fences.
You don't have to just driill posting trot and trotting in two point with no stirrups and extreme short (jockey) stirrups to build a leg although those are two definite ways to get a leg! Put out a series of ground poles approximately 6 feet apart. Get in 2 point and trot into the poles moving your hands forward and back to the rhythm of the strides. The distance your hand moves along the neck should not be extreme. Don't throw your hands forward, nor bring them back behind your shoulder. Once your hand is moving independently, it makes it easier to work on your leg. Another good thing is to post to the trot for 5 strides and then 2 point with half crest release for 5 strides (as long as your horse maintains a rhythm without contact.). This exercise will help you move from one position to the other. If you feel unstable in your upper body doing this exercise, you're probably pinching with your knee. Go back to walking in two point and the trot remembering to relax your hips and knees to follow the motion of your horse through the barrel.
Overall my suggestions would be to just leave the cross rails alone until you are able to trot and canter on the flat, moving through 3 point, half seat and 2 point with independent legs, seat and hands. That's not to say that this rider doesn't appear to have potential. Her mount looks willing enough from this picture. The rider has taken great care in providing her horse with leg & hoof protection. She has prepared her own appointments well with a helmet and body protector, boots and gloves. I do not know how long this pair has been schooling cross rails so my suggestions are based completely on this picture with no assumptions to the ability of either the rider or horse. Good luck, keep up your safety habits and always try to end on a high note!