Hendry began his career at Dundee before joining English side Tottenham Hotspur in 1990. In April 1991 he scored on his debut in an away defeat at Carrow Road versus Norwich City. A few weeks later he scored a memorable goal, equalising against Manchester United at Old Trafford on the last day of the 1990–91 season, two days after Tottenham had won the 1991 FA Cup Final. Two years later he had a similar impact as Tottenham played rivals Arsenal at Highbury on the last day of the 1992–93 season; Hendry scored twice as Tottenham won 3–1, though Arsenal had rested players ahead of their participation in the 1993 FA Cup Final.