Glover started his career with Nottingham Forest in 1987. Under the management of Brian Clough, the club were competing for the First Division title in 1987–88 and 1988–89. He was an unused substitute in the 1989 League Cup final victory over Luton Town. He was sent out on loan to regain fitness following an injury in the 1989–90 season. In September 1989, he joined Leicester City on loan, and scored once in five Second Division games for David Pleat's Foxes. In January 1990, he had a spell on loan with Mel Machin's Barnsley, and made 12 goalless appearances for the Tykes in league and cup competitions. Forest could only post an eighth-place finish in 1990–91, but found greater success in the FA Cup. Glover played at Wembley in the 1991 FA Cup Final, in what finished as a 2–1 defeat to Terry Venables's Tottenham Hotspur.