You can say, I'm Northern Irish 저는 북아일랜드 사람이에요. or I'm from Northern Ireland 저는 북아일랜드에서 왔어요. I think when you introduce yourself as Northern Irish to Koreans, you are asked to introduce the historical background of Northern Ireland. Usually Korean people don't know why you are a citizen of UK, even though you live in Northern Ireland. I hope this answer would be helpful for you.