Once you're inside, you need to quickly take cover and take out the enemies.
After taking out the enemies, look for the stolen vehicle. The stolen vehicle will always stand out and you will be easily able to identify the vehicle. Approach the vehicle to identify it.
Enter the vehicle and start driving towards the garage door to exit. When you reach near the garage door, you will be attacked by some more enemies.
You need to quickly take cover and take them out before you can use the keypad by the garage door to unlock the garage door.
You can also let them kill you. Once killed, you will spawn right back outside. You can use this opportunity to heal yourself and equip your armor before you head back inside to kill the rest of the enemies.
Once unlocked, get back into the vehicle and drive into the marker to exit the garage.
When outside, just drive back to The Agency garage to complete the mission. You will also get chased by some enemies, ignore them and keep driving to the agency. They will eventually lose interest in you.
Completing Security Contracts is important for progressing to the main Dr. Dre storyline.
Once you've completed at least two contract missions, you'll unlock access to the VIP Contracts. For more on The Contract DLC, return to the main hub.