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This can depend on the size of your plants and the variety you are growing.

The link below will help you with pruning information.

https://www.gardeningknowhow.com/ornamental/shrubs/holly/trimming-holly-bushes-how-to-prune-holly-bushes.htm

It is possible that it is scale or mealybugs, which produce honeydew that attracts sooty mold fungus (the black you see). I like to treat both with neem oil. It is very effective and safe. It will also help treat the sooty mold problem too. These articles will help:
https://www.gardeningknowhow.com/problems/pests/neem-oil-uses.htm
https://www.gardeningknowhow.com/plant-problems/pests/scale-bug-how-to-control-plant-scale.htm
https://www.gardeningknowhow.com/plant-problems/pests/mealybugs-white-residue-on-plants-leaves.htm
https://www.gardeningknowhow.com/plant-problems/disease/how-to-get-rid-of-sooty-mold.htm

Ideally the Holly would have been repotted while it was dormant.
It sounds stressed at this time, so I would go ahead and make the move to a larger pot and fresh soil.

I would only move up the pot size by 1 or 2 sizes. Generally a 15 to 20 gallon container will work for a slow growing Holly. Make sure it has adequate drainage.

You can use a commercial potting mix for acidic loving plants.

Water the plant enough to keep the soil moist but not muddy.

Your Holly may continue to lose leaves, but should recover once it settles into the new container.

Here is an article that has more information on some of the common issues with Holly.
https://www.gardeningknowhow.com/ornamental/shrubs/holly/diseases-of-holly-bushes-pests-and-diseases-damaging-holly-bushes.htm

Your plant looks pretty tough.

It was likely stressed from the transplant and may not have received enough water.
Do the stems bend or break and snap off?

You can also do the bark scratch test to determine if the plant is still alive.

https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-scratch-test.htm

The time it takes for the root system to get going again after transplanting can vary greatly. As long as the main trunk and branches still look good, and the branches are still bendable without breaking or snapping when lightly bent, it should still be fine. Water the tree with some water that has both a good root stimulator and a product called Super Thrive mixed into the same water the next 4 to 5 times it needs watering. The root stimulator will help get the root system going and the Super Thrive while helping with that as well, also helps the tree deal with the transplant shock and stress.