Moon began playing rugby during his time at St Joseph's College, Ipswich where he studied from age five to fifteen.[1] He earned a three-year scholarship to Sedbergh School to complete his A Levels and further his rugby development.[2]
In 2015 Northampton Saints confirmed that Moon would join their senior academy and he was subsequently awarded a senior academy contract at the start of the 2015/16 season.[1][4] In November 2016 he made his senior club debut against Newcastle Falcons in the Anglo-Welsh Cup.[1][5] Moon was also a member of the Northampton Wanderers side that beat Gloucester United 36–15 to win the 2017 Premiership A League[6] and Exeter Braves the following season to retain the title.[1][7]
In February 2019 Moon signed his first professional senior contract with the Saints[8] and later that season started for the Northampton side that defeated Saracens in the final of the Premiership Rugby Cup.[9]
On 30 January 2024, Moon would leave Northampton to join French side Bayonne in the Top 14 from the 2024-25 season.[10]