Summer can be a stressful time for trees and shrubs due to the heat and possible droughts. Make sure you are watching them diligently for signs of trouble.
Summer is the hottest and driest of the seasons. You will need to watch your trees and shrubs more carefully, especially in times of drought. Keep an eye out for wilting. You may want to set up a watering system to help keep them watered enough.
You can fertilize if needed (test your soil if you notice stunted growth, discolored or dead leaves, or wilting) in early summer. You should take care with using nitrogen fertilizers in late summer - they will promote new growth which may be damaged in winter.
Focus more on simply removing dead, diseased or damaged branches. Many trees and shrubs are more prone to diseases if pruned in late spring or summer.