I forget the names of them, but there are a couple of npcs around the great hall that give out quests.
The female klingon in the bar, half way up the ramp
The male klingon in the southern tech room, with the ground equipment vendors, typing on a console
The male klingon administrator in the duelling hall, north of the BO vendor
Alternatively, hail the KDF from your journal and you'll be able to get the missions from them there.
The first npc give you what is currently the only series of PvE style missions - which have you grind the signals in the Khaless Expanse not too far from Quo'nos. The rewards are Exploration medals which can be traded in the great hall.
The others give you pvp achievement missions - die a certain number of times, kill a certain number of enemies etc. The rewards themselves are not that great, but the rewards from the pvp matches themselves are very good, and the medals from them can be traded at the station in the Eta Ertani block.
But that's about it at the moment. More should be coming soon.