What can I do about holes in Viburnum leaves?

You've obviously got some kind of infestation by a pest which is munching the leaves as it grows. You could try spraying it with a pesticide, but it'd be a job and a half, probably best undertaken with your own large sprayer and a mix you've bought and made up yourself, rather than a shop bought bugs spray bottle.

Could it be viburnum beetle? Particularly like Viburnum tinus and V. lantana. The RHS has info on how to deal with it.

Mine gets it every year, it looks unsightly but the plants health is never affected and it soon gets over it. Perhaps try feeding and watering it especially in prolonged dry spells, to give it a boost. Wont help with the pest, will will toughen up the plants defences.

With so many large holes I would say it's leaf cutter bees. They make a nest like large cigars. I had them in some rat tail cacti in the greenhouse, they entered the pots through the drainage holes. I took cuttings off the cacti and hung the pots in the apple trees.

Leaf cutters make large holes, i assume mturnbulls are tiny a few millimeters in size

Can you put up a photo for us mturnbull, it would help identify.
3 years ago vine weevil killed off some very large viburnum, the infestation smelt like rotten potatoes. If the holes are very small it could be shot hole borer.