Sullivan was a goalkeeper from 1988 to 2013. Sullivan began his career with Wimbledon in 1988 and remained there until 2000. It was during his time at Wimbledon that Sullivan was acknowledged as one of the best goalkeepers in the league. He was selected for the division’s 1997-98 team of the season. In 2004, Sullivan moved to Leeds United where he was voted as the club’s Player of the Year in his first season.