[8] At the conclusion of the season, Klefbom signed a three-year entry-level contract with the Oilers and considered coming to North America for the 2012–13 campaign.

[9] In his third season with Färjestad BK, Klefbom began strong and earned time on their top pairing with either Chris Lee or Ville Lajunen.

[10] However, his promising season was cut short due to a season-ending shoulder injury that was the result of a crash into the boards during a game on 9 October.

[13] After attending the Edmonton Oilers development camp, Klefbom began his first season in North America with their American Hockey League (AHL) affiliate, the Oklahoma City Barons.

[14] During his time with the Barons, Klefbom worked on improving his overall game including "winning the battles in the corners" and "staying strong in front of the net.

[20] The emergency designation was eventually dropped[20] and Klefbom made his NHL debut the following day against the Minnesota Wild, where he recorded one assist in a 4–3 shootout win.

[21] A few games later, Klefbom tallied his first career NHL goal within 8:26 of the third period to lead the Oilers to a 4–3 overtime victory over the Anaheim Ducks.

When speaking about his improvements, coach Craig MacTavish stated: "[h]e just gives you 20 minutes of flawless hockey, and he’s had a great effect on Justin (Schultz).

[29] Klefbom began the 2015–16 season playing exhibition games with fellow Swede Adam Larsson on the Oilers’ top pairing.

[31] While his finger healed, the coaching staff kept him out of the lineup through February in order to improve his skating, lung capacity, and energy levels.