Potts was born in Hetton-le-Hole, County Durham, as was another well-known name in football, Bob Paisley.
Potts joined Burnley, who had one of the first youth-development systems in football; however, his own development was interrupted by the outbreak of the Second World War in 1939, which came before he could make his début for the club.
He wore the number 10 shirt associated with that position, and played in all but two of Burnley's 42 games in the Second Division that season, becoming the club's leading goalscorer with fifteen goals.
After working for Wolverhampton Wanderers as chief scout, Potts took the more senior position of manager at Third Division South side Shrewsbury Town.
In 1963, when forced to sell Jimmy McIlroy to raise funds for the club, Potts's relationship with Burnley fans suffered.
After leading Sunderland 1–0 with only seven minutes to go in their final match of the season, the team lost 2–1 and missed out on the third promotion place, which was filled by Carlisle United.
[1] Potts bought wisely but expensively, most notably on players such as John Evanson, Wyn Davies and Paul Hart.
The club demanded an instant return of results, and Potts walked a tightrope for the remainder of his Bloomfield Road career.
By the end of the 1975–76 campaign, chants of "Potts out" began to be heard, and with the team managing to finish only 10th, the board sacked him in May.
As of 2013, Potts is the joint-ninth (with Ian Holloway) longest serving Blackpool manager in terms of Football League games in charge.
In 2001, a section of Brunshaw Road which runs past the stadium was renamed "Harry Potts Way" in his honour.