Tarpey began his career at
Henley Town, where he played for two years in the senior team before joining
Basingstoke Town in 2007. After two years with Basingstoke, he joined
Hampton & Richmond Borough to seek more frequent first-team football. Tarpey broke into the first team following loan spells with
Walton & Hersham and
Chertsey Town, before joining
Farnborough in June 2012 after turning down a new contract at the Beveree. Tarpey scored 13 league goals in eighteen months at the Yellows before his contract was cancelled in January 2014 by mutual consent. He then re-joined Hampton. For the 2014–15 season, Tarpey joined
Maidenhead United. After 36 league goals in his first two seasons, he scored 44 goals in 41 league games in the 2016–17 season as Maidenhead won the
National League South, a new record for the league. He turned down an offer from
Coventry City in summer 2017 and signed a new contract with the Magpies. He opened his first season in the
National League with seven goals in his first six games, before signing for
Barnet on 31 August 2017 which enabled him to leave his full-time job as a fire & security alarm installer. Tarpey injured his
anterior cruciate ligament in his second appearance for the Bees, ruling him out for the remainder of the 2017–18 season. Tarpey returned from injury in October 2018 before re-joining Maidenhead on loan on 26 November 2018. On 4 February 2019, Tarpey reunited with former manager,
Alan Dowson at
Woking on a 28-day loan. He scored his first goal for the club in his second appearance against
East Thurrock United. He returned to Barnet and scored for them for the first time on 19 March against
Harrogate Town. Tarpey turned down the offer of a new contract from the Bees and left the club at the end of the 2018–19 season in order to return to part-time football. On 23 May 2019, it was confirmed in an interview by Alan Dowson that Tarpey would be rejoining
Woking on a permanent contract for the following season. He scored nine goals in 51 games for the Cards before joining
Isthmian League side
Bracknell Town for the 2021–22 season. Following just one campaign in
Berkshire with Bracknell, Tarpey announced he would be leaving the club in May 2022, with thirty appearances and nineteen goals to his name. On 18 May 2022, after leaving Bracknell, Tarpey opted to join newly-relegated,
Leatherhead for the 2022–23 campaign. On 17 August 2023, Tarpey joined
Hungerford Town on a short-term loan. Tarpey was then loaned to
Gosport Borough in September 2023. On 15 November 2023, Leatherhead announced that Tarpey was leaving the club amicably and by mutual consent, with the player's desire to get more first team football being a key reason. Two days later, Isthmian South Central rivals
Marlow announced that Tarpey had joined the club. On 17 October 2024, Tarpey announced his retirement from football after rupturing his
anterior cruciate ligament as well as suffering ligament damage. He was then appointed as attacking coach at
Reading City, before being appointed assistant manager ahead of the 2025-26 season. Tarpey also returned to playing that season. ==Career statistics==