In order to acquire the Supra you must complete 1 event first, a Speed challenge event. After completing this you are placed in a street race which you must win in order to acquire the Supra.
Beat the Supra in the race and the Supra is yours, Press
to get in the Supra and return it to the garage.
This is also the first time you get Nitrous, if you use it all in the first half of the race you can unlock