Murley made his Harlequins debut against Scarlets in the Anglo-Welsh Cup in January 2018. A powerful runner with an eye for the try line, the wing has represented England U18s and England U20s, as well as enjoying a steady rise in the pecking order at Harlequins. During the 2019/20 season, he scored seven tries in 20 games and became a Premiership champion in 2021, having started the final against Exeter. The Premiership's top try scorer for the 2022/23 season with 15 tries, Murley was included in several England squads, including England A. He started for England A against Portugal in February 2024, when he scored a hat-trick, before facing Australia A and scoring twice to translate his try-scoring prowess to the international stage. The wing was named in Steve Borthwick's squad for the 2025 Guinness Men's Six Nations and scored a try on his international debut against Ireland. He was recently called into Borthwick’s training squad ahead of England's summer tour of Argentina and the USA.