Roots are invisible but essential. Anchoring, hydrating, supplying essential building blocks for every bit of the plant, you can't really overestimate their importance.
Whenever you transplant, take off most of the leaves so they aren't demanding too much water from the roots. New leaves will appear soon.
You. don't even have to cut back the branches of a valued shrub. Just take off some of the smaller twigs and about half the leaves and it will be fine.
Planting from a container? The roots are often curled around and around inside it, a condition called being "root bound." Gently pull them out, if you can, so they will spread into the new soil. If there's just an impenetrable mass, cut off the outer quarter inch or so to give them a fresh start.
And always add a root stimulant to the first watering if the roots have been damaged. My favorite is SuperThrive and no, I'm not compensated for my recommendation. I tried it because I heard such amazing stories from customers at a nursery where I worked and I've used it for years. Things just grow better.