Air Leap was founded by the same owners as the airline FlyViking. After FlyViking ceased operations in January 2018, the virtual airline Next Move was founded in March 2018 to continue operating the Ørland - Oslo Gardermoen route. Next Move was renamed Air Leap after the company bought parts of the bankrupt Swedish airline Nextjet. The parts of Nextjet became the Swedish Air Leap, but lacked an Air operator's certificate (AOC) to operate the Swedish routes, which is why all flights in the beginning was operated by Denmark's Danish Air Transport (DAT), the Estonian NyxAir and the Dutch AIS Airlines, among others. On 11 June 2018 flights were resumed in Sweden. On 19 October 2018, the Swedish Transport Agency awarded Air Leap Air Operator Certificate (AOC) and registered the company as the official operator of three Saab 340Bs. The first flight under new AOC took place on 21 October 2018 from Stockholm-Arlanda to Mariehamn.