In November 2015, after featuring on the bench for Leyton Orient, Sargeant joined Redbridge on a work experience loan.[3] 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.[4] 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.[5]
In early January 2018, Sargeant moved to Isthmian League Premier Division club Margate on a 28-day loan.[6] After four appearances, keeping two clean sheets, he was recalled to Orient after Dean Brill picked up an injury in training.[7]
On 9 February, Sargeant signed on loan to Leatherhead until the end of the 2017–18 season.[8] He joined Barnet on loan for the first two months of the 2021–22 National League season, returning to Orient after ten appearances.[9]
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.[10] His sole appearance came in a 1–0 defeat away to Boreham Wood before leaving the club later that week.[11]
On 1 July 2022, Sargeant signed a new one-year contract to stay at Leyton Orient. Manager Richie Wellens said, "Sometimes when you’re looking for a number two keeper, chemistry is important. Sarge is a really good character, trains very well, and can be relied upon if we need him."[12]