The Old Kingdom quests are few and far between it seems, and no quest chains needed.
- Funky Fungi. From Ooze-covered Fungus which is a drop from a Savage Cave Beast inside the instance.
- The Faceless Ones. From Kilix the Unraveler.
It looks like you can just roll up to the Azjol-Nerub area, pick up the quests and get going in either Azjol-Nerub or The Old Kingdom.