Do not hold on with your knees😂 work on you core and hold on with your lower leg/heel wrapped around her sides. Also build up calve muscles - heel raises on a step/ledge are really good.
What you could do is hold on with your knees, you will soon start getting comfortable and will slowly release the reins and get a good hand position over the fence
Just remember to grab mane and keep your weight in your heels
Keep your heals down so you dont loose balance
Neck strap or leather for sure
Hi! Do leg strengthening exercises like no stirrup trot and canter so you can tighten your legs more when you jump and don't fall off.
I used to use an old stirrup leather as well, to stop over releasing. Although its kind of opposite problems it definitely has the same affect
Use an old stirrup leather and put it around your horses neck and use it as a neck strap. At the college I attend it is compulsory to use these in every ride. Simple but effective tool. Maybe also do smaller jumps just so you can get used to her scopes jump a bit more:)
what I would do is hold on to the mane until you get stronger