FC Midtjylland Kristensen was promoted to the first team squad in summer 2016 at the age of 18 and signed a five-year professional contract. At the age of 18, Kristensen got his official debut for FCM on 7 March 2016, in a
Superliga match against
FC Nordsjælland. He started on the bench, but replaced
Václav Kadlec in the 39th minute in a match, which FCM lost 1–2. He turned into a key player for the team in the 2016–17 season.
Ajax On 23 January 2018, Kristensen joined
Ajax on a four-and-a-half-year contract.
RB Salzburg in July 2021. After one and a half years with Ajax, Kristensen moved to Austria and joined
Austrian Football Bundesliga club
FC Red Bull Salzburg on a five-year contract.
Leeds United On 8 June 2022, Kristensen joined
Premier League club
Leeds United on a five-year contract for an undisclosed fee in the region of £10 million. He joined the team from 1 July 2022, and became Leeds's second confirmed arrival of the summer transfer window, reuniting with former Salzburg teammate
Brenden Aaronson. On 18 March 2023, he scored seconds after coming on as a substitute in Leeds’ 4–2 win at
Molineux against
Wolverhampton Wanderers.
Loan to AS Roma On 14 July 2023, Kristensen joined Serie A club
AS Roma on a season long loan. He made his Serie A debut a month later, on 20 August, in a 2–2 draw with
Salernitana. Later that year, on 3 December, he scored his first goal and provided an assist in a 2–1 away win over
Sassuolo.
Eintracht Frankfurt On 19 July 2024, Kristensen signed for
Bundesliga club
Eintracht Frankfurt on loan with a purchase option worth €15 million. On 16 April 2025, it was announced that Kristensen will move to the club on a permanent contract when the summer 2025 transfer window opened. ==International career==