Mac Allister was born in Santa Rosa on Christmas Eve 1998. His father Carlos Mac Allister had been a professional footballer in Argentina, playing as a left-back and winning three international caps earlier that decade. Mac Allister, who can trace his ancestry to Ireland, joined Argentinos Juniors youth set up, making his first team debut as a seventeen-year-old in October 2016. His two older brothers were already at the club and they appeared together on the pitch for the first time in November 2017.

In January 2019 Mac Allister signed for Brighton but was immediately loaned back to Argentinos Juniors for the remainder of the season. He spent the first half of 2019/20 on loan at Boca Juniors, scoring one goal in a Copa Libertadores tie and also being selected for the national side for two friendlies. The loan spell was meant to last the season but he was recalled in the January transfer window. He made his debut as a substitute at Wolves on 7 March, only for the season to be curtailed by the Covid 19 pandemic. When it resumed in June he made eight further appearances, all behind closed doors.

Mac Allister played 21 Premier League games in 2020/21, scoring once. At the end of the season he was included in Argentina's squad for the delayed 2020 Olympics in Tokyo, playing all three group games as they were eliminated on goal difference. The following season he featured far more for Brighton, scoring five times in 31 league appearances and was also recalled to the national side for the first time in over two years. In 2022/23 Mac Allister became a key component of a Brighton side that qualified for Europe for the first time in their history. He took over penalty duties, scoring a 99th minute winner against Manchester United from the spot in April. The attacking midfielder had enjoyed a memorable 2022/23 campaign, being named Brighton's player of the season as they finished sixth in the Premier League, their highest ever placing. In the mid season World Cup, held in Qatar, he scored his first international goal in a 2-0 group stage win over Poland. Argentina reached the final, in which Mac Allister set up Angel de Maria's goal that made it 2-0. Argentina eventually won on penalties but he wasn't needed to take a kick as he had been substituted during extra time.

Towards the end of the season speculation was rife about Mac Allister's future, even though he had signed a contract extension at Brighton until 2025. Liverpool moved quickly to secure his services, agreeing a deal less than a fortnight after the season had ended. He told the club's website after formalities were completed "It feels amazing. It’s a dream come true, it’s amazing to be here and I can’t wait to get started. I wanted to be in the first day of pre-season, so it’s good that everything is done. I’m looking forward to meeting my teammates. It was a fantastic year for me – World Cup, what we achieved with Brighton – but now it’s time to think about Liverpool and try to be a better player and a better human being every day." Alexis Mac Allister joined Liverpool from Brighton in June 2023 in a deal reported in the media as £35 million.

Mac Allister was an integral part of Liverpool's midfield during 2023/24. He was first used as a defensive midfielder but when Wataru Endo become more accustomed to the pace of the Premier League, Mac Allister was moved further forward. He scored some stunning goals, including a curling effort at home to Fulham and a piledriver against Sheffield United. A fine debut season was capped off with success in the Copa America with Argentina.

In the 2024/25 season, Mac Allister emerged as one of Liverpool’s most influential midfielders, combining technical intelligence with a winner's resilience. Operating primarily as a deep-lying playmaker, he dictated the tempo of matches with composure and vision, while also contributing defensively with unrelenting energy. What sets Mac Allister apart is his blend of qualities: a battler who takes knocks and quickly brushes them off, yet also a clever, tactical player who reads the game astutely and knows when to make decisive passes or runs. Mac Allister's season was punctuated by moments of individual brilliance, most memorably a sensational long-range strike against Tottenham that sealed the league title. The Argentine has established himself as Liverpool's midfield engine and one of the best midfielders in the world. His talent earned him a nomination for the PFA Player of the Season award for 2024/25.