Appears to be a Cornus or dogwood of some type. Not sure which grows in your area but would look at Cornus sericea to start, as it has a hugely wide distribution.

I can't even see clearly whether it is opposite or alternately arranged. Can you provide a picture of the whole shrub and a better view of the leaf arrangement? At the moment my best suggestion is Rhamnus cathartica, Common Buckthorn, which you definitely do not want to encourage. Common Buckthorn.

I think buck-thorn also.

I think those of you who mentioned buckthorn may be right. The edges are
finely serrate which means it's not dogwood. The leaves don't look as
rounded as buckthorn - more flattened ovate - but it's worth not
encouraging it, if so, because it's invasive. It definitely tried suckering at the bottom, and keeps trying to come back, so I keep having to cut it back aggressively. Too bad... It's one of the few things that wants to be in that corner of my yard. I will try to cut it to the ground and get a hydrangea in there instead. Thanks everyone!

European/Common Buckthorn. It's got to go!