Gunn says of the move south: "Norwich was easy to settle into, a bit like Aberdeen in many ways—a city surrounded by lovely countryside and lots of farms." However, since he joined the club partway into the new season, he initially found it difficult to take over as first-choice goalkeeper. Gunn had been bought as a replacement for England international goalkeeper Chris Woods, who had moved to Rangers F.C. Meanwhile, reserve team keeper Graham Benstead made a series of good performances and Norwich were top of the league. Ken Brown wanted to be fair to Benstead and made Gunn wait. A 6–2 defeat at Anfield proved to be the catalyst for Gunn's promotion to the first team. He made his debut in a Full Members Cup win against Coventry City, conceding a penalty, and made his league debut in a 2–1 victory against Tottenham Hotspur at Carrow Road on 8 November 1986.