The trick to successfully removing your suckers/water sprouts, without resprouting, is to take advantage of a characteristic in plants called "apical dominance". Essentially the leading bud (apex bud) on any limb is releasing a growth suppressant hormone that follows gravity and keeps dormant all the buds below it. This is why you can change direction of a branch by pruning back to an optimally facing bud, which will "wake up", and become the new apex bud. If you climb up into your tree and see a little village of sprouts all shooting up in a ring around an old cut, they will come back if you remove ALL of them. However, if you leave one or two of the strongest ones, per grouping, and cut them back to a bud that may turn into a viable branch some day, than that bud will help to suppress the sprouting of new suckers below it. Sometimes new suckers are the only wood you really have to work with if you're trying to reinvigorate an old tree, if you cut all of them off you would be dooming the tree to only having its elderly branches to do all the work of making energy for the tree, etc. I will commonly train suckers into someday viable new branches, as long as they aren't cluttering up the center of the tree or have something else negative going on with them. You still need to cut them back to a reasonable length though because they are only anchored in as many layers of cambium as the sprout is years old. Stiff wind or a large raven might break it right off if its not stubby for a couple years. Other ways to remove them would be to do some summer pruning while you're up thinning fruit anyway (fruit thinning being a super beneficial thing to do for healthy fruits, trees, and consistent yields). Summer pruning helps control/redirect vigor, but is not usually needed. Do it lightly and limit yourself to damaged limbs, suckers, etc. No unnecessary formative pruning. Hope this was helpful.