Introduced to rugby union at Cargilfield Preparatory School in Edinburgh, he was moved on to Merchiston Castle School. He played for Currie and Edinburgh Academicals, before moving south to go to study at Exeter University. He then played for the university rugby union team Exeter University.
He was signed by Exeter Chiefs in season 2022–23.[1] He was given a dual registration with allowed him to also play with Plymouth Albion in the first year, and then Cornish Pirates in the second year.[2]
On 15 May 2024 it was announced that he had signed for Glasgow Warriors for season 2024–25.[3] He became Glasgow Warrior No. 364 on his competitive debut in a 17 - 15 win over Scarlets at Scotstoun Stadium on 29 November 2024.[4] Richardson said: "It went really well. Can’t beat a win on debut. It feels pretty good. I wanted to rise to the occasion. I felt like it was pretty seamless and something we’ve been training for. Being a team like Glasgow, everyone is trying to do the same thing all the time. Everyone is on the same page. Even when there’s a switch in personnel, everyone’s one mind. I think that really brings cohesion to the squad. It was brilliant. I’ve never played in front of a crowd this loud, so it took a bit of getting used to. When the noise rises, you really feel the push and the energy from the crowd."[5]
He has represented Scotland U20s in both the Six Nations Championship and World Championship matches.[6]
He was capped in the Scotland 'A' international match against Chile on 23 November 2024.[7]
He was called up to the Scotland squad for their summer tour in 2025. He played in their non-cap match against Māori All Blacks, but made his senior debut playing against Samoa on 18 July 2025.[8]