He rode the Giro for the first time in his career in 2021. He finished 31st while riding in support of Romain Bardet, who finished in 7th overall.
During the 2021 Vuelta a España Storer won the first grand tour stage of his career on stage 7 and then went on to win again on stage 10. With this he became just the 2nd Australian, after Michael Matthews, to win multiple stages in the Vuelta.[9] On stage 7 and then again on stage 18, when he went on a solo attack of about 70 km before being caught on the final climb, he was awarded the combativity prize for the stage. With his attack on stage 18 he also took over the lead in the King of the Mountains competition and held onto the jersey thereafter winning the competition outright.