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. At 11, Arsenal were keen to sign him but refused to pay a compensation fee
In December 2019, it was reported that Aarons "went for a trial at Tottenham, rejected a contract at Luton, and his trial was unsuccessful, so he turned down the contract at Luton then Tottenham rejected him. It didn’t work out so that’s how he ended up at Norwich after a year or so out of football." He also trialled with Chelsea and QPR during this time. When without a club, Max travelled from his family home in Milton Keynes to a Powerleague facility in north London several times per week for one-on-one, after-school training sessions with Saul Isaksson-Hurst, a personal coaching specialist known to his father, Mike, with a decade of experience as a youth coach at Tottenham and Chelsea.
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.
At the end of August 2019, Max was called up by England's Under-21s for their clashes with Turkey and Kosovo in September 2019. He played the full 90 minutes on 6th September as England beat Turkey 3-2.
in late 2019, he was heavily linked with a January 2020 move to Spurs who had reportedly scouted him many times. On December 18th, it was reported that West Ham were considering an £18m bid. January 2020 saw continued speculation with Everton, Arsenal and Borussia Dortmund linked as well as Tottenham.
Aarons made 40 appearances for Norwich in 2019/20 as the club were relegated from the Premier League finishing bottom.
On 27th July 2020 it was reported by Sky Sports Germany that German giants Bayern Minich and Bayer Leverkusen were interested in signing Aarons, with suggesting that Munich would use him as cover for French international Benjamin Pavard. Closer to home, Wolves and Tottenham have also been linked. A fee of 20 million Euros has been suggested.
On 19th September 2020 it was reported that Spanish giants Barcelona had approached Norwich but that no firm £20m bid had been made. Transfer expert David Ornstein claimed that the youngster’s representatives had already agreed personal terms with the five-time European champions and that one of the bids could have been worth £20million plus potential add-on fees. Supposedly the bids included a season long loan with no option to buy. Ornstein clarified that Barcelona’s first bid was a loan with an option to buy, but no financial penalties based on appearances, with the second a loan with an option to buy but including those financial penalties if Aarons isn’t getting game time.
In February 2021 reports began to circulate that Bayern Munich had begun negotiations with Norwich regarding signing Aarons for £35m. Norwich had rejected an offer from an overseas club in January 2021 according to Stuart Webber. Manchester United have also reportedly scouted Aarons extensively in recent weeks as they look to bolster their right-back positions ahead of next season. It was later revealed that it was Italian side Roma which had bid for Aarons. He was then linked in late February 2021 with a move to Everton.(who were reported to be preparing a bid as Ancelotti is looking for a new right-back) and AC Milan.
On 22nd April 2021 it was reported that West Ham were keen on Aarons who had allegedly been told that he is free to leave the club this summer for the right price; a promise made by the club when Aarons chose to stay in the summer of 2020. The following day saw reports that Everton were stepping up their interest with reports of advanced talks and negotiations.
On 28th April 2021 he was named in the EFL Championship Team of the Season. He was also nominated for the EFL Championship Young Player of the Season but missed out to Reading's 19 year old midfielder Michael Olise. Aarons made 45 league appearances (and two Cup appearances) as Norwich won the Championship title in 2020/21.
The next club to be linked with Aarons was Inter Milan who were linked by Tutto Mercato Web on 1st June 2021 The website's chief editor Marco Conterio reports that Inter see Aarons as a potential replacement for Achraf Hakimi, if the Morocco international does join Paris Saint-Germain. Over the weekend of 17th/18th July 2021 Aarons was linked to Spanish champions Athletico Madrid if Kieran Trippier chose to return to England. Arsenal were also linked with Aarons seen as a replacement for Hector Bellerin.
On 9th September 2021 the Daily Telegraph reported that Aarons was the subject of a late bid from Borussia Dortmund who submitted a loan offer with an option to buy on the penultimate day of the transfer window. City 'instantly rejected' that proposal, according to the report.
He made 35 appearances in 2021/22 as Norwich finished bottom of the Premier League.
At the end of May 2022 former Manchester United star Rio Ferdinanc stated publicly that he thought United should sign Aarons. Newspaper reports also suggested that United would involve their starlet Ethan Laird in a deal for Aarons.
On 22nd July 2022 it was reported that Everton boss Frank Lampard was preparing a £15million bid for Aarons but that Borussia Monchengladbach and Wolfsburg were also interested. Marseille were also reported to have made an approach.