Harris began his career in the youth academy of Hereford FC, progressing into their under-18 side ahead of the 2016-2017 season. The keeper made three appearances for the Bulls during the season, while also appearing for West Midlands (Regional) League Premier Division side Pegagus Juniors on dual registration.
He spent a week training with Aston Villa in August 2017, and was sporadically involved on the Hereford FC bench for the first half of their Southern League Premier Division campaign during 2017-2018. He also featured twice for Hellenic League Premier Division side Lydney Town during the season.
In December 2017, Harris signed for League One side Oxford United on a two-year scholarship, joining their under-18 side.
Harris spent his first year solely at Oxford, before getting his first loan move away to Staines Town in October 2018, making three appearances for the side over the course of a month.
He played two games for Hellenic League Premier Division side Abingdon United during the early stages of December, before a month’s loan with AFC Totton in the Southern League Division One South & West in December 2018 saw him get eight more games of senior experience under his belt.
Harris appeared in Oxford United’s first-team squad for the first time in April 2019, an unused substitute in the U’s 3-2 win away at Shrewsbury Town in League One.
He signed his first professional contract in July 2019 and spent the first half of the season with the under-21s, before getting his final experience of senior football at Oxford as an unused substitute in their penalty shootout defeat away to Exeter City in the EFL Cup during December 2019.
He signed for National League South club Oxford City on a month’s loan in January 2020, making four appearance before returning to The Kassam Stadium.
Following his release by Oxford in the summer of 2020, Harris signed for League Two side Cheltenham Town in September 2020 after a successful pre-season trial.
He was an unused substitute 27 times for the Robins during 2020-2021 as Michael Duff’s team won promotion to League One, and he made his Cheltenham debut as a half-time substitute in the 2-0 EFL Trophy win at home to Plymouth Argyle.
In August 2021, Harris joined Southern League Division One South side Cinderford Town on a month’s loan where he made three appearances, before making four appearances and being an unused substitute four times for Southern League Premier Central side Redditch United after joining them on a month’s loan in September 2021.
Harris has also been recognised on the international scene, appearing for England Schools and England Colleges during the 2016-2017 season while a youngster at Hereford.
In October 2021, Harris joined the Seagulls on loan to cover for Luke Purnell’s suspension, going on to make his debut in the 3-1 win over Chesham United at The Optima. On 1st January 2022, Max’s loan was extended until the end of the season. During his six months with the Seagulls, Max appeared in 33 games and kept 12 clean sheets along the way.
In July 2022, the keeper returned for a second spell at The Optima on a season-long loan deal from Cheltenham Town.