You get the mission "Go to Dromund Kaas" after completing the mission "A Map for the Future"
Open your mission log:
Go to Dromund Kaas
Lord Zash wishes to tell you more about her plans for the map you retrieved; however, she feels she cannot do so on Korriban. Instead, she will meet with you in her chambers on Dromund Kaas, the capital of the Sith Empire. Head to the transit shuttle pad at the far end of the Valley of the Dark Lords and take a shuttle to the Imperial Fleet.
Since you are packing your bags and leaving Korriban, if you have any active missions now is the time to complete them . It is recommended to at least do the heroics before you leave, as you get good XP and rewards. Any missions that you do not plan on doing, you should abandon through the mission panel, so that they do not clutter up your mission log.
Exit the Sith Academy, go south and then east towards the shuttle. Climb the ramp and interact with the shuttle door to board the departure shuttle. Select the Imperial Fleet as your destination.
Arriving at Dromund Kaas completes the "Go to Dromund Kaas" mission and starts "Onwards to Dromund Kaas". But before beginning on the new mission, make sure to wander about the Imperial Fleet Main Level. There are many points of interest there, including:
Lord Krillis who gives you the advanced class training option which will let you become either a Sith Assassin or Sith Sorcerer and gain access to powerful skills and powers.
Crafting trainers, who can teach you crew skills.
A bounty board, giving you various quests to help you learn new game concepts such as social points.
A Galactic Trade Market (Auction House)
Cargo storage where you can store your items
You don't have to do all of the above, but you should definitely do the advanced class training mission and become a Sorcerer or Assassin. Then, you can continue on to the next mission, "Onwards to Dromund Kaas".
