A defensive midfielder, Nørgaard began his career in his native Denmark with BK Heimdal and Espergærde IF, before entering the youth system at Lyngby in 2008.

[3] He progressed to win three calls into the first team squad during the 2011–12 season and made his only senior appearance for the club as a substitute in a 2–2 Superliga draw with HB Køge on 20 November 2011.

[16][17] On 28 May 2019, Nørgaard moved to England to join Brentford on a four-year contract, with the option of an additional year, for an undisclosed fee,[17] reported to be £2.8 million.

[18] Wanting to "fall in love with football again", the move reunited Nørgaard with his former Denmark youth and Brøndby head coach Thomas Frank,[19] who had initially made contact with him during the previous season.

[23] Nørgaard began the 2020–21 season as a virtual ever-present in midfield and winning senior international recognition with Denmark,[24][25] but an ankle injury suffered during a match versus Preston North End on 4 October 2020 prevented him from making all but one appearance during the following four months.

[24][29][30] An injury restricted Nørgaard to only one appearance during Brentford's 2021 playoff campaign,[24][31] which culminated in promotion to the Premier League after a 2–0 victory over Swansea City in the Final.

[38] Nørgaard was affected by a persistent achilles problem during the regular season,[40] which did not require surgery and after playing through pain mid-season,[41] the issue seemed to resolve itself.

[48] During the 2023–24 pre-season, Nørgaard was left out of the club's 2023 Premier League Summer Series squad,[49] but he made a goalscoring return to match play in a behind closed doors friendly versus Lille on 5 August 2023.

[50] Again a starter when fit,[4][51] Nørgaard made 33 appearances and scored two goals during the 2023–24 season,[52] in which Brentford finished in 16th place, albeit 13 points clear of the relegation zone.

[4] On 8 September 2020, Nørgaard made his debut for the senior team with a start in a 0–0 Nations League draw with England and his performance was recognised with the DBU's man of the match award.