Disinfect bypass pruners in a solution of 10 percent bleach -- 1 part bleach mixed with 9 parts water. You might need a pair of lopping shears for thinning thick branches, but bypass pruners are generally all that's required.
Thin out as many as one-third of the total branches if the prince holly is dense and crowded. Remove dead or diseased branches first -- disinfect pruners after cutting diseased wood. Eliminate rubbing or crossing branches, as well as those that grow toward the center of the plant. If the holly is still crowded after removing these troublesome branches, select additional branches to remove based on placement to maintain a uniform shape. Cut branches back to about 1/4 inch above a branch union.
Trim individual branches back to make the holly bush the desired size -- remove no more than one-third of a branch's length in a single season. Make downward angle cuts on the stems at a leaf set so the cut is unnoticeable and water drains away from the exposed cuts. Some branches might be especially long compared to the rest of the plant, so trim them back to a more uniform shape. "Blue Prince" hollies are meant to be 6 to 8 feet tall and 3 to 6 feet wide so if you want to maintain a smaller size, it's best to replace the plant with a more compact variety.