West worked his way through Wasps’ Junior Academy while a pupil at Radley College prior to joining the Senior Academy in 2015.[3][4] He made his club debut in an Anglo-Welsh Cup game at Sale Sharks, and his Premiership debut at home to Saracens in January 2018.[5][6]
Despite making his league debut for Wasps in the 2017/18 season, West would spend the best part of two seasons on loan at Championship side Nottingham, making only twelve first team appearances across three seasons heading into the 2019/20 campaign.[7] He started in the 2020 Premiership Final as Wasps finished runners up to Exeter Chiefs.[8]
Wasps entered administration on 17 October 2022 and West was made redundant along with all other players and coaching staff.[9] On 19 January 2023 he was signed by Leicester Tigers until the end of the 2022-23 season.[2]
On 8 April 2023, West signed for Premiership rivals Saracens ahead of the 2023-24 season.[10] On 8 May 2024, West would leave Saracens to sign for rivals Northampton Saints ahead of the 2024-25 season.[11]
In January 2021 West received a call-up to the senior England squad prior to the 2021 Six Nations, after prop Joe Marler withdrew from the group for family reasons.[15][16]