The shrub has patches of dry leaves that looks like disease or insect.
How Do You Treat Sky Pencil Holly Disease?
Certified GKH Gardening Expert
Here is a link that lists common problems with Holly.
Trim away the dead and diseased material and dispose of. Clean any plant material from the ground also.
I would treat with Neem Oil. This works as both an insecticide and fungicide. It is safe for people, pets and bees.