I have an appendix, who I trained when he was 5. When I first got him, (he didn't jump) but him and I were both learning, so I rode literally every day (since he was a lunatic! No joke!) in draw reigns to get both of us used to eachother. Then, my trainer started him over fences (just basically teaching him to get over the fence) and I jumped every day. I wouldn't ride until he was dead, but just enough to where we were both understanding our job.
However, your horse doesn't sound green (lucky you!!). I would jump probably 2 or 3 times a week, and flatting the rest. Do a LOT of no stirrups (trust me, this makes your world 100% better!) The better your flat, the better the fences!
Good luck with your horse!(: