You get the mission "The Final Trial" after completing "Sith Arithmetic".
Open your mission log:
The Final Trial
Darth Baras has decreed that your final trial shall be to enter the tomb of Naga Sadow and recover an ancient lightsaber from a reliquary. Before you can enter the secret chamber that hides the reliquary, you will need to know how to open the door to the chamber, and for that, you need the slave Vette. Go to the jail in the Sith Academy and speak with Vette and Jailer Knash.
Go to the Jail. Jailer Knash is torturing the slave, Vette, using a shock collar. He tells you he has heard the rumors that you might become Lord Baras's apprentice. If you had spared Klemral, Knash informs you that he has not showed up yet and asks you if you know where he is. Tell him that Klemral is a good man, means well and tried hard.
Knash heard you'd be relieving him of this Twi'lek. Vette understands that none of you can figure out how to activate the tomb statues to open the forbidden cavern. She asks you if you got some kind of business in that secret Sith chamber. Your options will be:
Don't ask questions
That's correct
You just earned another shock (DARK)
If you choose the third option, you earn 50 dark points as Jailer Knash shocks Vette again. He gives you the shock control collar. He has set it to a higher level. Vette tells you that she can play tomb tour guide, but that she is officially on strike when it comes to domestic duties. You can now say:
Obey my every command.
Don't be silly
No, you aren't [SHOCK VETTA]
Choosing the third option, gives the higher setting a "test run" and you 50 dark points. Vette is now released from the cell. She says she'll take you to the unlocking points throughout the tomb then open the secret door for you.
Your mission log is now updated:
Vette knows the locations of secret activation points located in Sith carvings throughout the tomb. Find the activation points of the four secret carvings in the tomb of Naga Sadow: the statue, the broken urn, the ruined sacrophagus and the armor rack.
At this point, Vette is unlocked as your companion and joins your party. Your task now is to make Vette activate the hidden swithces (0/4). Exit Sith Academy, and locate the Tomb of Naga Sadow to the NE. Enter the tomb. Sith acolytes fill the tomb of Naga Sadow. They will strike you down, unless you dispose of them first. Eliminate 12 competing acolytes to complete the bonus mission "Eliminate the Competition".
If you look at the map, you will see the four activation points spread on a straight crossing the center of the tomb from south to north. First, make Vette activate the statue. Next, have her activate the broken urn. Then, have her take care of the ruined Sarcophagus.
Enter the Forbidden Cavern. Vette informs you that this is it, the secret entrance to the hidden cavern is here, she looks around to get her bearings. Vemrin attempts to sneak up on you from behind. If you helped Klemral earlier, he enters and warns you about Vemrin. You turn and kick Vemrin to the ground. Vemrin then will kill Klemral. If you did not help Klemral, you will notice Vemrin yourself.
Vemrin wants to kill you, and then have the slave girl show him the forbidden cave so that he can claim the lightsaber and his rightful place as Lord Baras's apprentice. Whatever you reply to him, leads to a fight. Defeat Vemrin, then speak to him again. your dialog choices are:
You were weak. Pathetic. (DARK)
You fought well (LIGHT)
Enough (DARK)
Ultimately, whichever answer you choose, leads to you killing Vemrin. Vette congratulates you on the nice work. You can shock her for some dark points if you want, but it will cost you some affection. She shows you were the secret entrance is. You can then either shock her (dark, -1 negative affection) or tell her you appreciate it (+15 affection). Your task now is to enter the secret chamber and recover the lightsaber from the reliquary in the tomb of Naga Sadow. Destroy 8 ancient droids standing between you and the lightsaber, to complete bonus mission "Naga Sadow's Honor Guard".
After entering the Reliquary and crafting your lightsaber, your task is to use it and varve your way out of the forbidden cavern. An optional bonus mission is also now available, "Sadow's Servants", to defeat the Entombed Warriors who awoke after you obtained the lightsaber. You can also use Quick Travel to travel to the Sith Academy. With the lightsaber recovered, it's now time to return to Darth Baras.
Eskella intercepts you at the entrance, accusing you of murdering her father. If you ask her to be more specific ("I kill many people's fathers") she tells you she is Eskella Gryton. Her father was Oveseer Tremel. She asks you if you remember killing him. You can respond:
Your father is alive (if you spared him)
Maybe [Show Tremek's ring]
Stay out of my affairs.
Second option leads to a battle.
If you tell her that her father is still alive and how you mercifully took her father's hand instead of his life, she vows to hunt down her father to end his humiliation. You can tell her:
If you must (LIGHT)
Spare him (LIGHT)
I don't think so (DARK)
You can try telling her to leave him alone and let him live in peace, but she is not convinced and is determined to kill him.
After this encounter, speak to Darhth Baras. He congratulates you for completing the task and claiming the ancient lightsaber. He asks about Vermrin. Choose the option "of course he did" for 15 affection points with Vette. Baras tells you that he sees you may indeed become one of the strongest Sith in the galaxy. Your trials are over. You are now his apprentice. This is only the beginning. With you as his right hand, we shall strike fear into the Empire's enemies. He must convene with the Emperor and inform him of your progress.
Baras gives you a shuttle pass that will take you to Dromund Kaas and asks you to meet him at the Citadel there. You can choose the option "My Regards to the Dark Lord" to gain 15 more affaction points with Vette. Baras tells you to take the Twi'lek slave as a gift. Do with her as you wish. If she'll be of use, by all means, take her with you to Dromund Kaas.
This concludes the mission "The Final Trial" and also ends your Sith Warrior trials on Korriban. Your next mission, "Leaving Korriban", takes you to Dromund Kaas.