What is good about the natural world is that sometimes it self-sustains. There are certain types of bugs that can keep harmful insect populations under control. Take for instance the ladybugs. They feed from aphids and other small pests. Likewise, lacewings, dragonflies and spiders also tend to eat harmful bugs. So, if you want to keep your tree safe from harmful insects, you will need to encourage the visit of these good insects.
Most of the time, the more variety of plants there is, the more type of insects come too. Then, you can plant more plants in your garden to encourage more visitors. You can even make some pollinators, like bees and beetles, to come to your tree. Another way to attract these bugs is to place a layer of mulch around the base of the tree (without actually touching the tree). This mulch will help spiders or other predators to hide from actual pests. Then, they can eat them too. And one more thing, try to control the use of pesticides that can be detrimental to some insects. If you still want to use it, choose an organic one, and better spray it directly onto the pests, and not all over the tree.