You do have a fungus problem which appears to be too late for spraying. These leaves should be dropping off in time and when they do bag them and discard. You can also, if practical for you snip off the affected leaves and discard the same way. You should find your holly coming back next year very nicely. Have you had a very wet spring up to now? I ask this since this weather condition and fungal attack go together.

it could also be a leaf miner. holly do suffer from a particular one.
peel the affected part apart is there a small creamy/white maggot inside it? if so then they need spraying with an appropriate insecticide.

Kudos to to Seaburngirl!!! I enlarged the photo for a closer examination of the effected leaves, it IS leaf miner.

slight advantage one of my hollies suffered from it a few years ago.