SWTOR Walkthrough - Seeking Darkness - Jedi Knight

You get the mission "Seeking Darkness" after crafting your lightsaber and completing the mission "Weapon of the Jedi"

Open your mission log:

Seeking Darkness
The Jedi Masters have sensed more darkness in the galaxy that must be stopped. Because of your efforts on Tython, you have been chosen to investigate. Head to the Jedi Temple spaceport and take a shuttle to the Republic Fleet. From there, you can arrange transport to Coruscant.

Your first task is to board a Shuttle to the Republic Fleet. Now is the time to either complete all your missions on Tython, or otherwise abandon them, as you won't be coming back to Tython for a while. When you are ready to leave Tython, head to level 2 of the Jedi Temple. Board the shuttle (By Interacting with the Shuttle Door) and choose "Republic Fleet" as your destination.



When you arrive at the fleet, your mission will be completed. But before leaving to Coruscant, take your time to check out the fleet station. Take the elevator to the main level of Carrick Station. There are numerous quest givers  and bounties here. You should especially talk to Master Nimi who will send you on a advanced training mission that will let you choose whether to become a Jedi Guardian or Jedi Sentinel. Crew Skills trainers are also located here.

This concludes the mission "Seeking Darkness" and starts the next mission, "The Jedi Envoy" which will take you to the Republic Capital of Coruscant.