KÍ Klaksvík notably became the first Faroese football club to play in the group stage of a major UEFA-organised European competition, qualifying for this phase in the 2023–24 edition of the UEFA Europa Conference League.

[2] In 1992, KÍ Klaksvík participated for the first time on a European stage,[3] competing in the Champions League preliminary round against Skonto Riga of Latvia, where they lost 6–1 on aggregate.

In the buildup to the 2013 season, Atli Danielsen and Meinhardt Joensen were signed, helping KÍ to reach the semi-final of the cup.

Later in the first half of the season, the team had implemented the style, playing attractive, free-flowing attacking football, eventually finishing fifth.

The Faroese club faced Swedish side BK Häcken in the second qualifying round, beating them 4–3 on penalties after drawing 3–3 on aggregate.

This result guaranteed the club's continental football path/route until at least December 2023 and meant they would also become the first ever Faroese side to play in the group stages of a European competition.

[10] Klaksvík then played the Moldovan club Sheriff Tiraspol in the Europa League play-off round, tying the home game 1–1 before losing 1–2 in the away match.

The Faroese team got drawn into Group A of the Europa Conference League 2023-24 season, along with Lille, Slovan Bratislava and Olimpija Ljubljana.