Greenbank has won gold medals as part of the 4 × 100 m Men's Medley Relay at the European, World Championships and Commonwealth Games.

He then competed at the 2014 Youth Olympics in Nanjing taking bronze in 200 m backstroke and gold in 4 × 100 m freestyle (with Duncan Scott, Miles Munro, Martyn Walton).

At the 2018 Commonwealth Games held at the Gold Coast, Australia, Greenbank won a silver in the 4 × 100 m medley with Adam Peaty, James Guy and Ben Proud.

He started the race in the backstroke leg, and the team finished in a European record time of three minutes, 28.10 seconds to beat the United States, and won their first gold medal in the event in the World Championships.

[7] At the 2020 European Championships held in Budapest in May 2021, Greenbank won a silver in 200 metre backstroke,[8] as well as a gold in the men's 4 x 100 m medley relay with Peaty, Guy and Scott.

[24][25] In the final, he won the bronze medal with a time of 1:56.15, finishing 0.53 seconds behind gold medalist Yohann Ndoye-Brouard of France.

[30] After finishing second in the 200 metres backstroke at the 2024 Aquatics GB Swimming Championships, Greenbank recorded a time that met the British Consideration criteria for a place at the 2024 Summer Olympics.