Both.

Without going into a religious Northern Ireland wank debate, I have duel nationality. I have a British passport, but I can also get a Irish passport if I want to.

Personally, I usually call myself Irish only because when I go out of the country and tell people I’m British they think I’m joking (accent I guess?), and the only people in the UK that do call themselves British are the English (and sometimes Welsh, I’ve never came across a Scotsman that calls himself British before Scottish). For everything else I say I’m Northern Irish, just to avoid ~drama~.