Born in Gloucester and educated at Churchdown School,[2] Sims is the grandson of former Cheltenham and England player Tom Price.[3][2] After playing for Longlevens RFC, he made his debut for Gloucester in the 1987–88 season, progressing to the first XV by November 1988.[3] He played for the club for 12 years, including captaining the team for two seasons.[3][4] He moved to Worcester for the 1999–2000 season before moving on loan to Bedford in January 2000.[3] In 2001, he captained the England National Divisions team against Australia at Welford Road Stadium.[5] He joined Exeter in 2002,[4] before moving on to Launceston RFC, Taunton R.F.C., and then after being released by Taunton joined Wellington RFC, where he filled a player/coach role and took the club to the Western Counties West league.[3][6][7] He then became head coach for the Withycombe RFC senior squads, while playing at lock for the 1st XV.[3][8]
Sims represented The Barbarians on three occasions, in 1995, 1996, and 1999.[3]