Class quests end at level 30, and then the guildmaster sends you to the related Job upgrade quest NPC for that class which takes over from your class quests. And those are every 3-5 levels or so (in ARC's case, the Job is BRD, and the NPC is found in the hollowed out log in the South Shroud along the path between Quarrymill and Bascaron's Druthers (he's the beadered elezen camper with the campfire inside).

He should have a quest available for you that rewards a 'Soul of the Bard', which will change your ARC class to BRD automatically upon equipping it. Then keep returning to that NPC every 3 to 5 levels to get a new Job quest which will reward you with new Job abilities, and.. from level 45-50, your first Job specific gear ('Artifact Armour' or AF).