He made his senior debut for the club on 26 February 2019 in a 6–0 league cup win against Stjarnan.

[citation needed] In June 2019, Hákon Arnar joined youth academy of Danish club Copenhagen.

[4] He made his senior debut for the club on 29 July 2021 in a 5–0 UEFA Europa Conference League qualifying round win against Torpedo-BelAZ Zhodino.

[5] On 17 July 2023, Hákon Arnar signed for French Ligue 1 club Lille, on a five-year contract running until 30 June 2028.

[8] On 2 September 2021, he scored twice in his team's 2–1 victory against Belarus in 2023 UEFA European Under-21 Championship qualification stage.