Who do i contact in Coruscant about a job in the empire?

[Trixie]

To actually join the Empire you need to complete one the faction quests listed in the Coruscant information thread that Luci linked. Once you've done that, where you go and what you do is entirely up to you as per the Coruscant FAQ. However, if you're looking to work for the Empire, one of those quests needs to be completed first. 

These are the three opening quests. 

Faction Quests

The Empire
Hand of the Empire OR There Are No Lines OR Empire Justice (must choose one)
Requirements: Not affiliated with the Kingdom, Pokemon Liberation Front or Rebels.
Difficulty: Moderate (5000-10,000 words dependent on writing quality)
Reward: Increased Influence with the Empire, 10% OM increase on Coruscant bounties

Hand of the Empire
Location: Coruscant, any tier
To prove your loyalty to the Empire, you will be required to work as part of the Empire Peace Division (EPD), a gigantic organisation in the Empire whose work ranges from military to domestic peacekeeping and enforcement. You must prove that you can be an asset to the Empire and carry out your tasks without showing doubt or hesitation. While day-to-day gangsters aren't too much trouble for stormtroopers, it's the Primes who make life most difficult. Find one of the Prime gangsters or dangerous revolutionaries in the lower levels of the city and take them into Empire custody where they can be interrogated (or deal with them in a more permanent manner). You have the jurisdiction to eliminate any who stand in the way of your objective. Do this and you will be granted more freedom and respect within the Empire - expect stormtroopers to salute as you pass - but know that you may also be targeted in other verses as you go about keeping the peace. Targets for this quest may be NPCs or PCs.
Unique Reward: Access to Stormtrooper or Imperial Officer uniform; allowed to request special Imperial Military quests

OR

There Are No Lines
Location: Coruscant, Tier 1
Empire Research and Development is one area of the Empire that is constantly being harangued for new ways to improve the city and help the EPD. Another way to assist the Empire is to help them with their experiments. Primes are difficult subjects to acquire, and all are unique and extremely valuable due to their ability to regenerate from any wound. If you are willing to submit your body to some ... tests in the name of the Empire, you will be sure to impress the Emperor. The specific nature of the testing will vary depending on your unique abilities, but expect to be pushed to your physical and mental limits. Do not fear the pain - ultimately, you will emerge from the testing a more powerful servant of the Emperor, and your loyalty may make you privy to secrets that ordinary citizens would not know.
Unique Reward: Access to Empire Research & Development; allowed to request special Empire R&D quests

OR

Empire Justice
Location: Coruscant (Various)
The Empire does not take an individual at face value. Your word is only as good as the actions used to back it up. Perhaps the official route is too much red tape for you. Maybe you're not a fan of eggheads or the shady science that goes on behind closed doors. Maybe you're just someone looking for a paycheck who sees a police state bursting at the seams with OM and you know where the goods can be found. Either way, you know that you want a piece of the Imperial pie. Earn it. Prove your willingness to serve the Empire in the here and now. Make a statement in some manner that shows where your allegiances lie. Join the Empire. Join the Future.