The first team Clemence played for was Tottenham Hotspur, for whom he made his debut against Manchester United on 10 August 1997, a match Tottenham lost 2–0. His season was cut much shorter by a four-day spell in February 1998, during which time Clemence picked up a red card against Barnsley. He involved himself to a greater degree the following season, displaying more of the form which won him a place in the England U21 side. He scored three times during his spell at Spurs, his first coming in the 1997–98 FA Cup against Fulham, followed by two league goals against Derby County and Sunderland. Despite not being part of Tottenham's squad for the 1999 Football League Cup Final he made three appearances during their victorious League Cup campaign.