[3] Eikrem was a regular starter for the United under-18 side in the 2006–07 season, and helped the team to the final of the FA Youth Cup, where they lost to Liverpool 4–3 on penalties after the two-legged match finished 2–2 on aggregate.

[5] A few days later, he played in his first game for the Manchester United first team, coming on as a substitute for Ryan Giggs in a 4–0 pre-season friendly win away to Dunfermline Athletic.

He was named as a member of a "B-squad" alongside several other younger players such as Will Keane, Joe Dudgeon, Oliver Gill, Ben Amos and Corry Evans.

[15] On 8 January 2014, Welsh side Cardiff City announced that Eikrem had signed a contract with the club, for an undisclosed fee and duration.

[20] On 22 February 2015, Eikrem scored one goal and made two assists in his first competitive match for the club, a cup fixture against Assyriska FF that Malmö won 3–0.

[24] The day after, on 26 July, he made his first appearance since returning to the club as a 65th minute substitute in a 3–0 home victory over Laçi in the Europa League.

Eikrem made his debut for the senior team when he replaced Markus Henriksen as a substitute in the 75th minute in a 1-1 friendly draw against Denmark on 15 January 2012.