[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.[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.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).[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.