Born in Norway, Ajer began his career with Raelingen FK before moving to Lillestrøm aged 11.

His first pro contract came at IK Start in 2014. His debut came in July that year. Aged 16, he became the youngest player to captain a team in the Tippeligaen.

In February 2016, he signed a four-year contract with Celtic in the Scottish top division. He spent a short time on loan with Kilmarnock at the start of 2017 but returned to his parent stay and became a mainstay in central defence.

In May 2018, he renewed his contract for a further four years. He would go on to win three Scottish league titles, the Scottish Cup and Scottish league cup in successive seasons between 2018 and 2020.

During the 2018-19 season, he was named in the PFA Scotland Team of the Year. That season also saw an international debut for Norway. He has since won over 20 caps for his national side.

After 176 appearances and six goals for Celtic, Ajer completed a move to Premier League Brentford in July 2021. He signed a five-year deal, making his full debut on the opening day of the 21-22 season during a 2-0 win over Arsenal.