You receive the mission "The Rescue" after completing "Kidnapped!"

Open the mission log:

The Rescue
Agent Galen is sending you to rescue Doctor Tarnis while he, Master Orgus and Master Kiwiiks secure vulnerable Republic weapons labs. Galen offered the services of a special tactical unit of Republic soldiers to assist you. Take a speeder to the Black Sun sector and speak to Sergeant Nidaljo and his squad at the Republic barricade to get their help.

Your first task in this mission is to speak to Sergeant Nidaljo. Board the speeder and choose the Black Sun Territory Taxi as your destination. Then travel toward the SW to the Republic Barricade. Fight your way through Black Sun attackers and reach Nidaljo. He seems to have many injured soldiers, as he instructs a corporal to get a kolto pack on one of them and the rest to prepare for evac. He tells you that Black Sun isn't a gang anymore, but an army. The Segeant and his men were securing a perimeter around the base for you, but Black Sun hit back with military grade weapons killing six of his men, seven with Jorin. Nidaljo says they are not equipped for this fight. They cannot help you.

Your dialog wheel now has the following options:
Calm yourself, Sergeant.
But they're just criminals.
I give the orders here.

The third option causes a loss of 1 affection with T7. Try the first option. Sergeant Nidaljo's forces have been fighting Black Sun for months. Now with new weapons and armor, the Black Sun are unstoppable. Nidaljo complains that his men are half-dead while Black Sun did not suffer a single casualty. There is no hope for victory. You can respond with:
There is always hope (LIGHT)
Not for losers like you
[Force Persuade] Follow me (DARK)

If you use the first option, you get 50 light points as well as 15 affection points with T7. You tell the sergeant that if he surrenders now, his soldiers would've died in vain. You inspire hope in the sergeant and his men, and they agree to help you. In the next dialog wheel, choose " May the force be with us" for 15 more affection points with your droid companion.

If you do the force persuade, you get 50 dark points. You tell Nidaljo that his men will doe everything they can to assist you. We're going to the base - now. Nidaljo is persuaded and orders his men to ration their medical supplies and give some to the Jedi.

The enemy has a computerized security network. Nidaljo and his soldiers will keep Black Sun forces busy while you take it out. Once it's down, they will make a frontal assault and clear a path for you. T7 will be confused by the Force Persuade you just did - "Sergeant = logic error // T7 = cannot resolve"

Your mission log is now updated:
Sergeant Nidaljo and his squad believe that Salarr is holding Doctor Tarnis at the Black Sun headquarters. However, he warned you will have to disable the defenses before you can get inside. Travel deeper into Black Sun territory and disable the security terminals outside their headquarters.

Your objective is to disable the Northeast, Northwest, Southeast and Southwest security terminals. Open your map and locate all the terminals in Lower Gangland, then go and disable them. While disabling the terminals, you can help the Republic secure the area outside the Black Sun's hideout by defeating the gang's forces in Black Sun Territory. Eliminate 10 Black Sun Forces to complete bonus mission: "Secure the Barricade".

After disabling the security terminals, you are now free to enter Black Sun headquarters in search of the kidnappers. Infiltrate the headquarters deep inside Black Sun territory and find Salarr. When you reach Salarr, you walk in as he is communicating with Tarnis. Turns out that Tarnis is a Sith and his kidnapping was faked. You approach Salarr, with the following dialog choices:
Tarnis? You traitor!
I saw this coming.
He's right, Salarr

If you choose the third option, you tell Salarr that his own people gave him up. Lord Tarnis says that Coruscant's fate is already sealed. One of Salarr's men approaches you from behind, but he is shot by Nidaljo's troops. Your options now are:
You can't win, Salarr
Glad you made it, Sergreant.
Open Fire! (DARK)

Either option leads to a fight. The third option gives you 50 dark points, you lose 30 affection with T7-01, and you immediately initiate a battle. Defeat Salarr and his men.

SWTOR The Rescue

Kira Carsen contacts you on the holocommunicator. They intercepted Salarr's holocall to Tarnis. The planet prison prototype here at the lab are a fake. Tarnis stole the real planet prison. In the next dialog wheel, choose the first option to tell Kira to trace that holocall she intercepted and us it to locate our Sith's base of operations.

In light of this, General Var Suthra wants you to report back to him immediately. Return to the senate tower and speak to General Var Suthra in Strategic Command. The General is furious about the spies. Tarnis's entire engineering team vanished along with the Planet Prison. They're all traitors too. Tell the General that we must remain calm, and get 15 affection points with T7.

Tarnis will use the Planet Prison against Coruscant. He could trap us here forever. Paralyze the Republic by holding us hostage. You're the only hope of stopping that. Your dialog options will be:
First I have to find him
Begin an evacuation
There's no one else?

If you suggest an evacuation, Var Suthra says it would cause mass riots. There are billions of people here with no way to leave. But Kira says she just traced that holocall we intercepted from the Black Sun base. Tarnis was communicating from down in sector 439, Justicar territory. Justicars are paramilitary vigilantes. They took over a sector, cut ties with the rest of Coruscant. And they don't like visitors. Many Justicars are ex-Republic military who came home to find gangsters controlling their neighborhoods. They believe the Republic abandoned Coruscant to crime, so they've taken matters into their own hands. But the Sith Lord is the greatest threat.

Kira suggests to come along and help you. This unlocks her as a companion. The fate of the Republic rests on your shoulders. Select one reward for completing the mission. This concludes "The Rescue" and starts the next mission, "Tracking Down the Traitor".