It’s difficult to give you some tips because if you are not going to be jumping for a while you really wont be able to practice.
Do you know why you are leaning/standing up?
How trustworthy is your horse?
If you comfortable with the idea , you can set up a grid of four or five ground poles set apart for the trot , tie your reins in a knot and drop your stirrups.
Put your hands behind your back or fold your arms across your chest and trot through the grid.
A long time ago, never mind how long. I took hunt seat lessons and actually jumped on purpose.
I was not really very good at it and had lousy timing and was either jumping ahead or getting left behind .
Why, you ask? Well, I tell you it’s because I was jumping with my eyes and trying to guess when the horse would take off, instead of letting the horse close my hip angle.
What really helped with that was cantering over a ground pole. Sometimes a horse will jump a ground pole but mostly they just canter over it. But it really allows you to feel the horses motion . It works even better if you do it without stirrups.
Very simple exercises but dont do them unless you feel confident.
Usually, working on an independent seat by doing some work with no stirrups will correct bad habits like allowing the shoulders to get ahead of the hips, or sitting unevenly .
And yes, you really need a steady unflappable horse who wont be bothered if you fall on his neck or slip to the side.
I would also watch some videos and watch what the riders do and their form over the jumps.
Good luck. Hope this helps.