Kolbeinn came through Víkingur Reykjavik's youth program and made his professional debut with HK Kópavogur at 16 years of age.
Kolbeinn began his career in Iceland with Víkingur, where he came through the academy, before deciding to move over to HK's youth team for a brief spell in March 2006 three days before he turned 16.
He made his professional debut for AZ on 5 August 2010 in a UEFA Europa League qualification match against IFK Göteborg.
After courting interest from Borussia Dortmund and Newcastle United, Dutch giants Ajax moved in for the player with a €2 million bid.
[11] In an interview, Kolbeinn stated that it was a dream come true to work with Dennis Bergkamp and Frank de Boer.
[13] On 30 July 2011, he made his first appearance in a competitive match for Ajax, as the team lost the Johan Cruyff Shield 2–1 to Twente.
He made his return to the Ajax side on 1 April 2012, coming off the bench to score the last goal in a 6–0 win over Heracles Almelo.
[18] On 2 July 2015, it was announced that Kolbeinn had signed a five-year contract with French Ligue 1 side FC Nantes, with Ajax receiving a €3.5 million transfer fee in the deal.
[22] Kolbeinn declined a move to IFK Gothenburg in the 2018 January transfer window over fears the artificial pitches in Sweden could cause more impact damage to his knee.
[33] That held true when Kolbeinn captained the side after Aron was carried off injured in a World Cup qualifying match against Slovenia in June 2013.
[40][41] Two days later, Guðni Bergsson the chairman of the Icelandic Football Association, resigned and Kolbeinn was expelled from the national team.
Six months later, when the police had still taken no action in Kolbeinn's case, Þórhildur's father realised that her daughter's perpetrator had been recruited on the Iceland national team for an upcoming match.
[47] Following the arrest of Gylfi Sigurðsson in July 2021, some disturbance took place in the Icelandic social media where unconfirmed cases of other sexual assaults were reported.
She even added that the Football Association had hired a lawyer who offered her a compensation and asked her to sign a confidentiality agreement to cover up Kolbeinn's case.
[50] Heavy protest arose in the Icelandic media following the interview, resulting in the resignation of Bergsson and the entire board of the Football Association.
[51][52] Following Bergsson's resignation, Arnar Viðarsson, head coach of Iceland, announced that Kolbeinn would not play in upcoming matches for the 2022 FIFA World Cup qualification.
[54] Henrik Jurelius, director of sports at AIK, claimed that neither he nor Björn Wesström, his precursor, had received any information on Kolbeinn's case when he joined the club in 2019.
An agreement was reached when Kolbeinn had consented to Þórhildur's and Jóhanna's offer of duplicating the payment and giving half of it to Stígamót, a center for survivors of sexual violence.
[57] On 2 September, members of Ultras Göteborg, an IFK supporter group, put up ribbons at Kamratgården stadium, demanding that the club annul Kolbeinn's contract.