Conner is a graduate of Forks High School.
In New Moon, Conner regularly sits at the lunch table with Mike Newton, and enjoys chatting about sports with him. He uninvites himself when Mike and Bella suggest a movie night together with some of their friends.
In Eclipse, he is part of the "them" or "bad" side, which hasn't re-accepted Bella for the months of depression she spent during Edward's absence. He was one of the graduate students and so was invited to the Cullens' graduation party.