Speak with Sergeant Cormun, behind a barricade of Crates, near the entrance to the Tomb of Ajunta Pall on Korriban. This is a level 1 quest.
Sergeant Cormun: Excuse me, acolyte. Sergeant Cormun. Fifth Infantry company. Korriban Regiment. Can I talk to you?
You can reply (Options might vary whether you are a Sith Warrior or Sith Inquisitor)
Permission Granted
Hurry Up
Is this necessary?
Choose the second option. He tells you that there is an opportunity for you for not just doing your class quest such as getting the Sith Warblade, but also start building ties to the Imperial Military. Sergeant Cormun is here commanding a hard target mission to exterminate K'lor'slugs in this tomb. They're horrific things. Mouths bigger than your head. He has already lost three squads of good men fighting them. They come in pack, they'll swallow a man whole.
You can tell him:
I have to go in there
"Good" men aren't enough
So what?
Choose the second option to tell the Sergeant his men need better training. He tells you that those men were battle hardened, but the enemy just has more numbers. The damn K'lor'slugs breed so fast there's no way to wipe them out conventionally. So they started targeting their egg chambers. They went insane. They managed to get explosives to all of the egg chambers, but the K'lor'slugs were all over them before they could detonate them. You can say:
Your tactics may be flawed
I'll finish the job
Why should I care?
Tell him you will finish the job. The Sergeant warns you not to underestimate those K'lor'slugs. They're smarter than they look.
Open your mission log to get the full details for the quest:
K'lor'slug Infestation
Sergeant Cormun commands an operation to exterminate the k'lor'slugs in the tomb of Ajanta Pall. He planned to detonate explosives in the k'lor'slug egg chambers, but his squad was wiped out after the bombs were set. Sergeant Cormun needs you to enter the tomb of Ajunta Pall, kill the k'lor'slugs and detonate the charges in the egg chamber.
You have two tasks:
Kill K'lor'slugs (0/6)
Detonate the Explosives
The K'lorslugs should be nearby. There are Large K'lor'slug Burrowers, as well as the smaller K'lor'Slug Broodlings that are easier to kill. Defeat six of them to complete the first objective.
Next, you want to detonate the explosive charges. These are found in the K'lor'skug egg chambers, to the Northwest. Open your map and find the mission marker. Enter the Egg Chambers, defeat any enemies in there such as the K'lor'slug Broodwatcher. Then click on the Explosives Detonator to detonate the bombs. This will destroy the eggs and complete the second objective. You now need to return to Sergeant Cormun. He congratulates you on outstanding work. He heard the explosives when you set off the charges.
As a reward, you receive credits, experience points, as well as a [green] item which can be different depending on your class (As a Sith Warrior, I got the Sith Dueling Boots). This completes the mission, K'lor'slug infestation.