I don’t have a picture of the pest, but I do have the damage. The tree is an American persimmon; I don’t see anything similar on the Rosseyanka next to it.
There are a number of these holes, mostly around 5-7 feet up on the tree. I wonder if this is why this tree seems to have so many dead branches each year.
Looks a bit like the work of a sapsucker. They peck out the holes and then eat the sap that oozes out and any bugs that get caught in the sap. They can be tough on a tree but I’m not sure if they’ll kill it.
Persimmons often “orphan” lower branches and they just die off. I had a bunch do that on my little Prok this winter and when I tug them they come right out, actually leaving a little hole where they came out, but these holes look like a sapsucker to me.
I haven’t dealt with this personally, but maybe try covering with something to protect those areas so they can heal? I’m thinking similar to vole protection.
I think any of the usual bird deterring methods might work, like putting a big fake snake in the tree, hanging CDs or foil pie plates, mylar reflective tape, etc. Sapsucker holes are referred to as “wells” and they usually return to the well to keep feeding as sap and bugs build up, so you probably should try to deter them. My neighbor has them hitting his holly and dogwood trees, but for some reason they leave my dogwoods, only 50 feet away, alone. He wrapped one trunk that was particularly hard hit in burlap, which has kept the birds off it, but I’m not sure it is something that might cause fungus or mildew on the bark. I really have no idea why they target a specific tree.
As @Evenfall mentioned, they probably won’t kill the tree, but the holes could be an entry point for disease and certainly for bugs, so I’d try to keep them away if possible.