Early Spring, before trees leaf out is a great time to inspect your woody plants. Without the leaves, you can see the branch structure, crossing/rubbing branches and branches where bark is missing to identify pruning that could improve the health of the trees and shrubs and their shape.
Another concern is for the plants growing in the shade of a tree. Thinning the tree (removing interior branches) or limbing it up (removing lower limbs) to allow more light to reach the plants below will improve the health of the garden without harming the tree or the beauty it provides.
If you are planning to plant in the tree ring or within the tree’s drip line, be sure to select shade tolerant plants in the smallest containers available to avoid damaging the roots of the tree. Unless the tree is in a wet area, plants that prefer dry shade work best because the roots of the tree will be competing with the plants for water and nutrients. Do not add more than 3” of soil and mulch or bury the root flare (so that the tree appears to be a pole in the ground).