A product of the Fylkir academy, Kolbeinn began his senior career with the club and transferred to FC Groningen in 2015, with whom he progressed into the reserve team.

[4] His progression was such that he became the club's youngest-ever player when he made his debut at age 14 years and 229 days in a 3–0 group stage League Cup victory over Þróttur on 11 April 2014.

[5][6] Kolbeinn signed a new 2+1⁄2-year contract on 2 May 2015, he became the youngest player in the club's history to start a Úrvalsdeild match,[7] when he made a late substitute appearance in a 1–1 draw with Fjölnir.

[12] On 17 February 2019, he won his only first team call up for an FA Cup fifth round match versus Swansea City and remained an unused substitute during the 4–1 defeat.

[13] Kolbeinn finished the B team season with 43 appearances and 9 goals and then returned to Úrvalsdeild club Fylkir on a two-month loan,[14] which was subsequently extended by a further month.

[12] On 20 August 2019, Kolbeinn moved to Germany to transfer to the reserve team at Borussia Dortmund on a three-year contract for an undisclosed fee.

[25] On 21 August 2024, Kolbeinn transferred to Eredivisie club Utrecht and signed a three-year contract, with the option of a further year,[26] for an undisclosed fee.

[27][28] Kolbeinn was a member of Iceland's 2021 UEFA European U21 Championship finals squad and he made three appearances prior to the team's group stage exit.