Glover was a strong, little right-back who was said to be gipsy-like in appearance. He was quiet and unassuming on the field and relied more on skill than brute force. Glover didn't make the first team at his hometown club, West Bromwich Albion, but managed to play 23 games for Blackburn's first team in his debut season at Ewood Park. Owing to injury and the emergence of future England captain Bob Crompton he moved south to join New Brompton (who in 1912 changed their name to Gillingham) in the Southern league. His contract was still owned by Blackburn Rovers as New Brompton was outside the Football League and was sold to Liverpool in May 1900. Glover experienced Championship success at Liverpool in the 1900/01 season, the first of 18 Division One titles for the Reds. Glover played in ten of the 34 matches that season replacing John Robertson, who returned for the last three games of the campaign.

Glover started the following year as first-choice, but was replaced half-way through the season by aforementioned Robertson. Glover reclaimed his place following Roberton's move in the summer of 1902 and missed only four of the 34 first division fixtures of 1902/03 which Liverpool finished in fifth place. At the end of the season Glover was caught accepting illegal financial inducements from Portsmouth to sign for the south-coast club. As a result he along with teammates Bill Goldie and Sam Raybould were banned from football until 31 December 1903 and from ever signing for Portsmouth. Glover left Liverpool in January 1904 despite Liverpool's offer of maximum wage for a new contract and played 124 League games for first division Small Heath from 1904-1908, until Birmingham (as the club changed its name to in 1905) were relegated in the 1907/08 season.