Born in Basildon, Morris attended New Hall School, where his performances caught the attention of Saracens. A boyhood fan of the club, Morris joined Saracen's academy when he was 15, following in the footsteps of his older brothers Vincent and Oli.[1] Morris joined Bishop's Stortford on loan during the 2015–16 season, where he gained his first experience playing senior men's rugby, and joined Rosslyn Park on loan during the 2016–17 season,[2] making his senior competitive debut for Saracens in their Anglo-Welsh Cup fixture against Scarlets on 27 January 2017.[1]
Morris' progress was rewarded with a contract extension announced in November 2017.[3] He gained further experience on dual-registration with Ampthill and Bedford Blues,[2] and played a key role during the 2018–19 Premiership Rugby Cup, in which Saracens were runners-up,[4] and during the 2018–19 Premiership Rugby Shield, which Saracens Storm won.[2] Morris made his Premiership debut for the club away to Wasps on 27 April 2019, and, in a match that was his first home premiership appearance, he scored two tries in a 38–7 win against Exeter Chiefs on 4 May 2019.[2][5]
Morris has spoken about his difficulties with injuries, which have disrupted his career.[1][6] He signed a new two-year contract with Saracens in July 2020,[7] and extended that deal for an undisclosed length of time in January 2022.[8]