He started his career at home side Washington United F.C. before transferring to Barnsley sometime prior to 1910. He played in both FA Cup finals that Barnsley reached in 1910 and 1912. In the first Barnsley lost in the replay to Newcastle. The second also went to a replay but Barnsley won, defeating West Bromwich Albion by one goal in extra time. The Manchester Guardian praised his play in the first match and in the replay Glendenning won the ball from a West Brom player and passed it to Harry Tufnell to score in the last minutes of extra time. 
In March 1913 he transferred to Bolton who he played a total of 83 games for as club captain. Bolton reached the FA cup semi-finals in 1915 where they were defeated by Sheffield United captained by George Utley his fellow wing half from Barnsley. In the 1916–17 season, Glendinning appeared as a wartime guest player with Burnley. After the war he played for Accrington Stanley.
After the end of his playing career he took up coaching and moved to the Netherlands. He would have a short spell, only one game, a 4–1 victory over Switzerland, as coach of the national side in 1923. He would then coach Koninklijke HFC until 1928. He was made the permanent coach of the Netherlands in 1925, holding both coaching positions up until the 1928 Summer Olympics when he choose to focus on the national team. He would remain the manager of the Oranje until 1940, leading them to the World Cup finals in 1934 and 1938. The tournaments would be disappointments, exiting in the first round on both occasions, to Switzerland by a score of 3–2, in 1934, and then to Czechoslovakia by 3–0, in 1938. Glendenning managed the Oranje through 87 games, with 36 wins, 36 losses and 15 draws. To this day he remains the Dutch national coach with the most victories. By comparison, the only Dutch coach Rinus Michels to win a major trophy, Euro 1988, had 30 victories from 53 games, over an 18-year (1974 to 1992) on again off again association with the national team. While Dick Advocaat managed 31 victories from 55 games and more recently Marco van Basten had 35 wins from 48 games before being knocked out at the quarter final stage of Euro 2008.
Glendenning's last game as a manager was the 4–2 victory over Belgium played on 21 April 1940, the game was also Abe Lenstra's second international cap. Three weeks later the Dutch national side would be in Luxembourg to play their next international match, but the game would never be played because of the German invasion of the Netherlands. He would pass away on 19 November of that same year. He is buried in Bolton (England) where the KNVB has maintained and replaced his headstone.