Two kinds of apple aphids commonly attack apple trees. One is evident by curled leaves, and the other causes white tufts on the tree. An outbreak often occurs because of the use of pyrethrins as a pesticide, which also destroys the aphid predators and parasites.
Take a look at your tree (assuming it is springtime). Does it have curled leaves? Unroll one. Inside you will likely find little bugs - aphids. You might also see ants marching up the trunk and branches of the tree. They are shepherds of this pest. This would be the Rosy Apple Aphid. Because they cause the apple tree leaves to curl, it is difficult to impossible to hit them with a spray. Biological control is a good approach.
The other one, the wooly apple aphid, looks like white bits of cotton on the branches and trunk. If you take a pinch of the white stuff and squish it between your fingers, there will be a red stain. They are red when they are squished. One of the insidious things about this pest is that it can infect the roots of the tree as well as branches. In the roots, they can cause root gall. A soap or oil spray may work better on these, as they are visible on the surface of the tree unless they are in the roots.
If you wish to spray, a good summer oil or soap will do. Again, the kind rolled up in a leaf will be protected from the spray.
There are several options for biological control. The first one that comes to mind for most people is the ladybug. Ladybugs do eat aphids, and it is worth noting that the ladybug nymphs are even more voracious. So if you buy ladybugs and then think they left the tree, maybe they did, but they also might have laid their eggs in the tree for the nymphs to take over. Ladybug eggs are yellow and are laid in an array on leaves. When they hatch, the nymphs look like tiny spiny alligators. They are pretty well camouflaged, so you might not ever notice them.
Another larval form of aphid eating bug is the lacewing. Lacewing larvae love to eat aphids. a second benefit is that they will also eat insect eggs they find - including codling moth eggs.
For both insects, it is a good idea to have a companion planting of small nectar flowers to support the adult populations. For example, plant Yarrow, Fennel, Dill, Lavender, Sweet Alyssum, Veronica, Lobelia, Sedum, etc. You can also buy nectar food in powdered form and spray it or sprinkle it around.
There is a parasitic wasp called Aphidius colemani. You can buy these. But first, take another look at those aphids in your tree. A closeup look will reveal whether or not you find mummies with a little round hole in them. These are the leftover bodies from a parasitized aphid. If you find these, then you already have the parasitic wasps.
Wooly apple aphids can be controlled by the parasitic wasp called Aphelinus mali. Parasitized aphids turn hard and black and have the exit hole.
Syrphid fly larvae will eat aphids. The adult Syrphid fly looks like a flattened bee with a hovering flight style. You may already have some of these around your yard.