Looks like Briar, but hard to say positively
Your comment prompted me to do a bunch of searching. When I was a kid, one of my friends' dad was a pipe smoker. I was admiring his pipe collection, and asked what the beautiful wood was. He said "briar." The only briar I knew of was from the old story about "Brer Rabbit and the Briar Patch." I ask him what a briar was, and he said it was a kind of rose. As I grew up, the kinds of briars I encountered were mostly red and black raspberries, which are related to roses, and whose canes are much like the branches of rose bushes.
When I was in scouts, and looking for something to carve for a neckerchief slide, I got a piece of rose bush root from a neighbor who was digging one up. Nothing like pipe briar. Later, I dug up some raspberries, and was again disappointed.
When you mentioned briar, I began searching. Much to my surprise, I found that briar also referred to an evergreen found mostly in the mediterranean basin, and also to smaller shrubs called heaths and heathers. No wonder I never found a piece of wood anything like pipe briar.
Learn something new every day.