At the start of the 2011–12 season, Norris joined Royston Town and played a number of games for the reserve team where his performances caught the attention of the first team manager. On 20 September 2011, he made his debut for Royston in a 4–1 home win against Haringey Borough. In 2012, he signed for Cambridge United on a 2 year deal and was loaned back to Royston Town for the duration of the season. Norris made his Football League debut for Cambridge in a 2–2 draw at home to Accrington Stanley on 11 April 2015. He made his debut for Wolverhampton on 8 August 2017 in a 1–0 win against Yeovil Town in the second round of the EFL Cup. In July 2019, Norris joined Ipswich Town on loan for the 2019–20 season. He made his debut for the club in a 3–1 loss to Luton Town in the EFL Cup and made a total of 20 appearances for the club during his loan spell prior to the League One season being ended early. On 19 May 2021, Norris made his league debut for Burnley in a 0–3 home defeat to Liverpool. Norris joined League One club Peterborough United on loan until the end of the 2022–23 season. On 16 January 2023, Norris made his league debut for Peterborough in a 2–0 away win against Port Vale, in June 2023, he signed a permanent contract with Peterborough. Norris has been wearing the OG's since 2015!