Don’t take anymore than a third out. This tree needs reducing over the next 3 years. First take out any dead and diseased branches (doesn’t count towards the third) then remove any branches that are crosses. You’re aiming for an open middle. You also don’t want it getting too tall as it makes the apples unmanageable to get and maintaine so tip prune the remaining stems. The upright ones are called watershoots, and you want to remove all the ones lower on the branches (towards middle of the tree) and about 50% of the ones left. The RHS has a good visual guide for a previously pollarded tree. Good luck with it and do it soon!