How To Access expansion if no one is doing Story Quest anymore?

[Xenos88]

Either Queue as a healer or a tank and that should get you into Qarn quickly.

[Enkidoh]

Or, just get another level 50+ friend (preferably level 60) and set the party to 'undermanned' and turn off level sync (by clicking the cogwheel icon in Duty Finder), thus allowing you to enter it at a higher level without requiring a full party.

Although there might still be some annoying aspects it should be fairly easy to steamroll unsynced at a high level (you could probably solo it as a level 50+, but duoing it makes it easier still), and you still satisfy the requirements for the main scenario doing it that way (the quest just requires you to complete the dungeon, and is not determined by how you enter it).

[Antonio_Xul]

I've soloed that dungeon as a tank to get credit of exploring the whole dungeon since I never did get in that extra room, so it's totally doable anytime passed 50.

[ADVSS]

When you get a level 60 friend to single handeldy melt a dungeon like qarn with you, youll understand why undersized party is probably one of the best additions from heavensward to date its all we ever really wanted from 2.0, and im actually glad it made its way to the game.period.

[Blitzace]

These dungeons are still being ran daily. Either by new people or by the roulettes.
You can also ask for someone to run you through it(They can in 5-10 minutes unsynced probably)