Beesley joined Wigan Athletic in September 1984, where he would spend five seasons playing in the then Third Division. He played 185 games in all competitions in five years at Springfield Park, before joining Leyton Orient for £175,000 in October 1989. A first team regular Beesley played 35 league and cup games at Brisbane Road in 1989–90, helping Orient to finish comfortably in mid-table in the Third Division under Frank Clark.
Sheffield United
Beesley was sold to Sheffield United for £300,000 in July 1990, at the time the highest fee paid for a player by the Blades. A regular in the first team he was instrumental in keeping United in the First Division in 1990–91 after their promotion from the Second Division the previous year. He played 49 times in 1992–93 as the club finished 14th in the inaugural season of Premier League football and reached the semi-finals of the FA Cup. A dependable player he was popular with the fans and was voted Player of the Year in 1993. Now no longer an automatic choice at centre back he was instead often asked to fill in at left back as the Blades struggled unsuccessfully against relegation the following season, and failed to make an immediate return in 1994–95. He eventually left Bramall Lane having made a total of 195 league and cup appearances in five seasons.
Leeds United
It came as some surprise when Beesley was sold to Leeds United in August 1995 for a £250,000 fee. He was used mainly as a back-up player by manager Howard Wilkinson during his time at Elland Road, starting just 19 top-flight games in close to two seasons at the club. Unable to dislodge either Lucas Radebe or David Wetherall, new boss George Graham looked to offloaded Beesley in 1996–97.
Manchester City
Beesley's next move was to Manchester City in February 1997 for £500,000, rejoining his former boss at Orient, Frank Clark. He played six First Division games for the Sky Blues in 1996–97 but quickly fell out of favour at Maine Road after Joe Royle succeeded Clark as manager. Beesley spent December of the 1997–98 season on loan at Port Vale where he made five appearances before returning to Manchester, and ended the campaign on loan at West Bromwich Albion, playing eight First Division games for the Baggies.
Released by City Beesley was allowed to join Port Vale on a free transfer in August 1998 where he was disciplined by the Football Association after he picked up 12 yellow cards in 36 games during 1998–99. He left Vale Park after new manager Brian Horton took charge, and signed with Blackpool in July 1999. Beesley's best days were now behind him however and he made only 18 appearances as the Tangerines were relegated into the Third Division at the end of the 1999–2000 campaign.
Chester City
Beesley signed with Chester City in July 2000 with then manager Graham Barrow describing him as "an outstanding professional". Playing more regularly than he had done at his previous club he was voted Player of the Season for 2000–01 by the Seals fans after his organizational skills helped Chester to boast the lowest goals conceded tally in the Conference. Despite this owner Terry Smith criticised Beesley for his positional play in an FA Trophy semi-final clash with Canvey Island and banished him to scouting duties – a decision Beesley described as "unexplainable".
Staylybridge Celtic and Ballymena United
Beesley moved on to Stalybridge Celtic in October 2001 where he played 26 times and was described as "magnificent all season" by manager Paul Futcher. However the club failed to avoid relegation out of the Conference in 2001–02, and Beesley left, finishing his career in Northern Ireland with Ballymena United.
Later life
Beesley worked as a youth team coach at Notts County, before he was appointed under-18 coach at Leeds United for a brief spell in 2007. In 2012 he was appointed as the kit man at Ipswich Town by manager Paul Jewell, before departing the role in July 2015.
