Growing up in Peckham, Stemp showed interest in the performing arts from a young age, attending musical theatre classes at Belcanto London Academy Theatre School. After professional training at Laine Theatre Arts, Stemp’s West End debut came in 2013 as an ensemble member in Wicked.
His first lead role came in 2016, when he was cast in a new production of Half a Sixpence at Chichester Festival Theatre. After critical praise, the musical transferred to the Noel Coward Theatre where it played for a year. For his performance as Arthur Kipps, Stemp received his first Olivier nomination for Best Actor in a Musical.
Away from the West End, Stemp has played Eddie in the international tour of Mamma Mia! as well as making his Broadway debut in Hello, Dolly!. He took over the role of Barnaby Tucker in 2018 from Taylor Trensch, starring in the production for six months until the show closed in August 2018.