FAI FLM working position to accommodate training and distracted by other duties; experienced a MVA separation event; indicating if the Supervisor/CIC position would have been staffed this event would not have occurred.

Narrative

FBK airport called for release of Aircraft X; IFR to FYU. I released Aircraft X with a restricted altitude of 3200 on departure; for two IFR aircraft overhead FBK on downwind for FAI. Aircraft X departed FBK. Aircraft X was RADAR identified and turned on course. I never issued the climb to final altitude. I became busy with 5 IFR aircraft just North of FAI who all needed turn to final. My scan was not sufficient to see that Aircraft X; who was in East RADAR's airspace was not climbing. After turning two aircraft to final; my scan took me back to Aircraft X. I immediately realized he was 3300 in a 3400 MVA; additionally the aircraft was 1 mile away from a 4000 MVA. I issued a climb to Aircraft X; and turned him Southeast bound away from the higher MVA. Recommendation; the major concern needing attention; is already being addressed by the FAA; additional staffing at FAI. As a FLM I was busy working position to accommodate training. I should have been working the FLM/CIC position rather than working a sector. Additionally; the CIC working was combined with East RADAR. If a stand alone CIC would have been in the operations area I believe this would have been caught prior to the aircraft entering the 3400 MVA.