You will get the mission "The Plight of the Acolyte" after completing the first Sith Inquisitor mission, "Of Mind and Matter"
Open your mission log:
The Plight of the Acolyte
Overseer Harkun has given you your second trial, but not many details. You must report to Inquisitor Zyn in the Academy jail to receive further instructions. Go to the Sith Academy jail and speak to Inquisitor Zyn.
The jail is in the west part of the Sith Academy. Locate it using your map. Talk to Zyn. He tells you that a short while ago, there was what they call an "unauthorized murder" here in the Academy. A rivalry among apprentices resulted in death. He wants you to interrogate the acolyte and make him tell you who committed this crime at any cost. Go and interrogate Alif. He begs you not to hurt him claims he does not know anything. You can tell him you are your friend, tell him to not resist, or, if you want to be really evil, tell him to Shriek in pain and shock him. The last option gives you 50 dark force points, and will make your character's force alignment go towards the dark.
If you shock him, you can then even be more evil and shock him again, or even ask him to sing something happy. Keep interrogating him. If you are interested in having your character go to the dark side of the force (which grants you access to certain gear) you can torture him further. Alif finally breaks and tells you that the murderer is an apprentice named Esorr Kayin. Kayin's master's a dark council member. Talk to Zyn again. He tells you that your trial here is done and that he will send his commendations to Overseer Harkun. You can express some concern for the prisoner, Alif, for some LIGHT Force points.
Your task now is to return to Overseer Harkun. He gives you and Ffon another trial. Both you and Ffon will have trials of intellect, trials that test your ability to apply your understanding of the Force to solve problems. He sends Ffon to the library on the second floor of the Academy to translate some texts for Lord Zash. To you he gives another task. Deep in the ancient, monster-infected tomb of Marka Ragnos, there is a holocron filled with dark secrets and encased in a great stone monument. No one has figured out how to release the holocron from its stone prison in over a thousand years. He wants you to bring the holocron to him, or die.
This ends the mission "The Plight of the Acolyte" and starts the next mission, "A Little Knowledge".