In June 2019, Hákon Arnar joined youth academy of Danish club Copenhagen. On 21 May 2021, club announced that he have signed a new contract with the club until June 2026. 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.
Hákon Arnar is a current Icelandic youth national team player. On 2 September 2021, he scored twice in his team’s 2–1 win over Belarus in 2023 UEFA European Under-21 Championship qualification stage.
Hákon Arnar was born into a family of footballers. His parents Haraldur Ingólfsson and Jónína Víglundsdóttir are former national team players. His brother Tryggvi Hrafn is also a professional footballer.
- As of 11 September 2021