There are several types of licenses in the game. Listed below are how many events you must win to get that class license. The wins do not stack from class to class, so you can do events over again when you achieve a new class.

D license: 2 wins
C license: 7 wins
B license: 16 wins
A license: 26 wins
Burnout Paradise license: 45 wins
Burnout Elite license: 110 wins