My guess is some kind of caterpillar. Each species is host specific. For example Monarchs only eat milkweed plants. Let's do some detective work...What kind of plant is this? Then research which caterpillars (maybe another insect) this plant plays host to? What does your gut tell you? Which insect is most likely the guilty party? Most of the time this is done overnight. Get a flashlight, bucket of soapy water & a pair of kitchen tongs. Go out at night and inspect the plant. Chances are you'll see who's munching away. Drop him into the bucket of soapy water (or throw him over the fence to the neighbor's side).

If you could post a picture of the whole plant for ID purposes, that would be helpful, unless you know what plant it is. It looks like it might be a Viburnum variety, and if it is, the likely culprit is Viburnum beetle, which only affects Viburnum and no other plants.

You don't have to kill everything Bathgate! But perhaps Viburnum beetle needs curbing.

I don't kill everything - don't be silly!