You get the mission "Race to the Ruins" on Coruscant after completing the mission "Tracking down the Traitor".
Open the mission log:
Race to the Ruins
Lord Tarnis has set up the Planet Prison in the ruins of the old Jedi Temple on Coruscant. You need to stop him before it becomes fully active. Use the elevator in the Justicar Territory to reach the Works, then travel to the speeded pad that can take you to the elevator that leads to the Jedi Temple. Once there, travel to the Jedi Council chambers to confront Lord Tarnis.
The elevator is south of the Justicar Checkpoint. If your companion disappeared or had otherwise left you, make sure to press "N" to bring up your crew window, then summon either Kira again, or T7. Then go to the elevator and take it to "The Works". When you arrive downstairs, open the map and locate the speeder to the SW. It is on the other side of the map, so make your way through the ducts and corridors of the works until you get there.
When you arrive, talk to The Works Taxi and choose Jedi Temple Taxi as your destination. When you arrive, travel north to the Jedi Temple Central Elevator and take it to the Jedi Temple Ruins, then enter the Jedi Temple Council Chamber, then head east. Imperial forces have fortified their position inside the remains of the Jedi Temple. In order to get to the Planet Prison in the former council chamber, you'll need to eliminate the Imperial opposition. Defeat 10 Imperial Forces on your way to Planet Prison to complete the bonus mission "Clearing the Council Chamber".
As you arrive at the council chamber, Lord Tarnis is communicating via a holo communicator with Lord Nefarid, Lord Sadic, Darth Angral (Tarnis's Father) and Lord Praven. He informs the Sith that he is departing Coruscant now. The Planet Prison deploys in minutes and the Republic will have no choice but to surrender. When he sees you he asks you if you have come to die, as he draws out his lightsaber. Your dialog choices are:
No, I've come to stop you. (LIGHT)
You overestimate yourself
It's you who will die.
The first option will give you light points. Second option won't give you light points but will give you affection points with Kira if she is your companion currently. Defeat Lord Tarnis. Then, disable the Planet Prison by interacting with the Planet Prison Prototype controls. Darth Angral is furious about you killing his son, and vows revenge on you and the Republic.
Your task now is to return to the Senate Tower and speak to General Var Suthra to inform him of these latest developments. He is telling Master Satele Shan that noone saw this coming. Satele accuses the General that if he had told the Jedi Council of his secret project, they could have averted this disaster.
You inform Satele and General Var Suthra that Coruscant is safe, but that you had to destroy the Planet Prison and kill Tarnis.
Public comm channels are being flooded with threats from Darh Angral bowing revenge. But the Empire has formally disavowed Darh Angral's actions, saying he's gone rogue. It's a lie, but the Senate refuses to authorize a military response. Neither the Republic nor the Jedi are prepared for another war. We would lose. Billions would die.
The General says that if the enemy turns our weapons against us, billions will die anyway. Tarnis transmitted the details of all our top secret projects to his father. The transmission was traced to the planet Ord Mantell. Darth Angral must have a base there.
Var Suthra informs you that he has one of his best starships waiting for you at the spaceport. Your astromech droid is prepping it for takeoff. There is a civil war on Ord Mantell. It's a no-fly zone. Dock at the orbital station there and contact Suthra.
Your mission log is updated:
Darth Angral, the father of Lord Tarnis, has vowed vengeance on the Republic for the death of his son. General Var Suthra has instructed you to meet with an SIS agent on Ord Mantell so you can begin your mission to stop him. Head to docking bay 74 in the spaceport, and once on board your ship, contact air traffic control using your new ship's holoterminal for clearance to leave Coruscant.
This unlocks your own starship, as well as a new companion, C2-N2. This companion can heal, but is not so good in fighting. Go to the Coruscant Spaceport and then to the Jedi Knight hangar to the Southwest. After the cutscene, board your ship to find yourself in the Defender Flight Deck. Your companion introduces himself as Seetoo Enntoo, steward of your vessel. C2 series droids represent the latest advances in everything from starship technical maintenance to nutritional advice tailored for your specific organic needs. Welcome aboard this Corellian Defender-class Light Corvette. It was custom-built to offer a Jedi both first-rate combat performance and meditation amenities. Along with the usual accomodations, you'll find a secure captain's locker for storing valuables. Your bridge contains an ever-updating map of the galaxy. It's quite beautiful to look at. Priority alerts from the Republic network are accessible at the HoloNet console. Long-range communications are available via the holoterminal. And the ship's intercom will inform your crew that you wish to meet.
You learn that C2-N2 is not equipped for physical danger. Its function is to maintain this starship as your home away from home. But it is happy to assist you with any non-hazardous task, such as modifying other technologies, long range surveillance and diplomacy, and prides itself on the utmost attention to detail.
Whenever you are ready to depart, consult the galaxy map on the bridge. The ship's computer will handle the rest. This also completes a small mission called "Introducing C2-D2" and gives you some experience points. You should now your ship's holoterminal and request permission to launch from Coruscant Control. Spaceport Official grants you permission, and coordinates to Ord Mantell have been uploaded to your navicomputer.
The reward selection for this mission includes a Tacticial Lightsaber, or a Coruscant Commendation. This concludes the mission "Race to the Ruins" and starts the mission "New Intelligence".