I would register Heavensward so you get awarded XP for the level 50 main scenario quests.

As for "going up a class," I see on Lodestone that you're already a dragoon (you may wish to update your forum display preferences to show that rather than lancer). Dragoon is as close to "going up a class" as a lancer gets. You do, however, unlock the three "extra jobs" of astrologian, dark knight, and machinist once you get far enough through the level 50 main scenario quests.