Given started his career at Celtic, however he never made a first-team appearance and he was released and signed by Blackburn Rovers on a free transfer in 1994. Given was part of both the Sunderland team who won the Football League First Division title in 1995–96 and the Swindon Town team who won the Football League Second Division title that same season, while on loan from Blackburn. He was signed by Newcastle United in 1997 for a fee of £1.5 million, and it was there that he began competing to be a first-choice Premier League goalkeeper. Given was part of the teams who came runners-up in the 1998 and 1999 FA Cup campaigns, and was named in the Premier League Team of the Season for 2001–02 and 2005–06. He played in the UEFA Champions League and UEFA Cup with Newcastle, and was involved in the club's title challenge in 2001–02. Although he submitted a transfer request during the 2000–01 campaign after losing his position in the starting line-up, it was denied, and Given went on to regain his place.