Stooke was called up to the England Saxons squad on 20 January 2014 as injury cover for Graham Kitchener.[1][2]
On 19 January 2016, it was announced Stooke would leave Gloucester for local rivals Bath Rugby from the 2016-17 Aviva Premiership season.[3] On 9 February 2016. Stooke was signed by London Irish on loan for the remainder of the 2015–16 season,[4] he returned to Gloucester for a few weeks in March/April[5] before returning to Irish for the remainder of the season.[6]
After a slow start at Bath, Stooke cemented himself as a reliable figure in the second row of the Bath scrum during the 2016/17 Aviva Premiership Rugby Season. Making 30 starts in all competitions.[7]
Stooke had his first taste of leadership, calling the line-outs on 16 February 2018 as Bath took on Newcastle Falcons at Kingston Park. Absent (on England duty) teammate, Charlie Ewels, ordinarily took the role.[8]
Stooke was the only player in the Bath squad to play in all 22 games, during the 2017-18 Premiership Rugby season.[9]
In March 2019 Stooke was called up as cover to England's Six Nations squad.[10]
On 10 May 2021, Stooke would leave Bath to join Premiership rivals Wasps from the 2021–22 season.[11]
On 20 May 2022, Stooke experienced a fibula fracture causing him to leave the pitch and to miss the rest of the season l[12]
Wasps entered administration on 17 October 2022 and Stooke was made redundant along with all other players and coaching staff.[13]
Stooke joined Bristol Bears on a short term injury cover deal at the end of 2022, before joining French side, Montpellier, during the 2022/23 Top 14 season.[14]
In November 2023, Stooke re-joined Bath until the end of the 2023-24 Premiership Rugby season.[15] On 11 July 2024, it was confirmed that Stooke has joined Japanese side Red Hurricanes Osaka in the Top League for the 2024-25 season.[16]
