Max was one of ten youngsters to join Norwich's Under-18s as first year scholars on 1st July 2016. Described as a pacy full-back, he was previously at Luton Town.
On 5th May 2017, it was reported that Max would be offered his first professional contract after breaking into the Under-23s during 2016/17.
After training with the first team during the 2018 pre-season, he made his first team debut on 14th August 2018, starting in the League Cup clash at Carrow Road against Stevenage which Norwich won 3-1. This was followed up with a start in the League Cup clash at Premier League side Cardiff City oh 28th August 2018 in which Aarons scored his first professional goal in a 3-1 win for Norwich. He was rewarded with a call up to the England Under-19 squad. His league debut came at Ipswich on 2nd September 2018 which finished 1-1. His first league goal came in the 3-1 home win over Rotherham on 1st December 2018.
On 10th September 2018 he made his England Under-19 debut, starting in a 2-1 win over Belgium.
On 10th October 2018 he signed a new deal until 2021 with the Press Association reporting that Chelsea and Arsenal had been keeping a close eye on his development. In late December 2018, the Sun linked him with a £15million move to Spurs with German side Red Bull Leipzig also reported to be interested.
On 26th March 2019, Aarons, along with Jamal Lewis and Teemu Pukki, were named in the Sky Bet Championship Team of the Season. The team was voted on by all 24 managers and head coaches from the Championship, with City having the highest representation in the eleven with three, ahead of Leeds United (2) and Sheffield United (2).
He finished the 2018/19 season with 43 appearances, scoring three goals, as the Canaries won the Championship title. During June 2019, he was constantly linked with a move to Manchester United who opted instead to sign Crystal Palace's Aaron Won-Bissaka for £45-50m.