Stevens was born in
Hillingdon,
Middlesex, He joined
Brighton & Hove Albion in 1977. Stevens made his debut as a 17-year-old on 15 September 1979, in the
First Division as Brighton won 2–0 at home to
Ipswich Town, the club which had released him as a schoolboy. A versatile
defender who could also play in
midfield, he made 26 appearances in his first season, scoring once, and remained a regular in the side. Losing to
Manchester United 2–1 with three minutes of normal time remaining, Stevens equalised, and teammate
Gordon Smith missed an easy chance to win the game at the end of extra time, remembered for the commentator's line "And Smith must score..." Brighton lost the replay 4–0, and Stevens joined
Tottenham Hotspur for a fee of "about £350,000". Stevens made his Tottenham debut at the start of the
1983–84 season, again against Ipswich, but this time was on the losing side. He was a first team regular that season, making 40 league appearances and scoring four goals, and played on the winning side in the
1984 UEFA Cup Final, scoring his
penalty in the
shootout against
Anderlecht. He was also in the side that suffered an unlikely 3–2 defeat to
Coventry City in the
1987 FA Cup Final. He was also
capped seven times by
England, and was included in the squad for the
1986 World Cup squad – as, confusingly, was the unrelated
Everton player
Gary Stevens. He later joked that Sir Bobby Robson picked them both to make sure he got the right one. He made two
substitute appearances in the tournament. Stevens left Spurs for
Portsmouth in 1990 but persistent injuries forced him to retire in 1992. He had never fully recovered from a knee injury suffered in November 1988 when heavily tackled by
Vinnie Jones. At the time of the challenge, Gary Stevens was contesting possession of the ball with
John Fashanu near the touchline when Jones slid into him. ==Post-playing career==