In November 2015, after featuring on the bench for Leyton Orient, Sargeant joined Redbridge on a work experience loan. Sargeant made his first-team debut, and kept a clean sheet, in Orient's 1–0 win away to Yeovil Town on 7 May 2016. After spending most of the 2016–17 season on Orient's substitutes' bench as back-up to Alex Cisak, Sargeant made his second appearance in the 2–1 defeat at home to Carlisle United on 4 February 2017. In early January 2018, Sargeant moved to Margate on a 28-day loan. After four appearances, keeping two clean sheets, he was recalled to Orient. On 9 February, Sargeant signed on loan to Leatherhead until the end of the season. He later joined Barnet on loan for the first two months of the 2021–22 National League season, returning to Orient after ten appearances.
On 11 January 2022, Sargeant joined National League side Wealdstone on a seven-day emergency loan deal due to a suspension to first choice goalkeeper George Wickens. His sole appearance came in a 1–0 defeat away to Boreham Wood before leaving the club later that week.
On 1 July 2022, Sargeant signed a new one-year contract to stay at Leyton Orient.