Piling mulch up around trees is a bad idea. Excessive mulch causes rot in the truck, creates a home for insects that attack the tree, and encourages the development of a secondary root system. A tree with a secondary root system in the mulch zone starts to depend on it, causing the primary, deeper root system to wither. That makes the tree vulnerable in a drought, when the soil is dry near the surface and the primary roots are no longer able to draw deep water. IF the primary root system dies, the tree loses its anchor and is at risk of toppling over in heavy wind or snow.
GrassChopper’s recommendation is to strip off as much of the old mulch as you can and top dress with a 1.5 or so of new mulch. If you start with the stripped beds and add 1 inch a year you’ll only have to strip them every 3 or 4 years. The goal is to keep the mulch layer less than 3 inches deep. If you haven’t fertilized recently, apply some balanced fertilizer to the stripped beds before you put down the new mulch. Make sure the mulch is pushed up against the trunk of the trees or shrubs when installing.