You can take a train from Åre to Trondheim via Storlien station in around 3 h 14 min.
How to get from Åre to Trondheim
From Aare station train to Storlien station then train to Trondheim S. 3 h 14 min 226 kr. From Åre station bus to Duved centrum, taxi to Storlien station, bus to Stjørdal stasjon, then line 38 bus to Dronningens gate. 5 h 22 min 328 kr. From Åre drive to Trondheim. 2 h 25 min 267 kr.