To increase the level on your license, you have to win 
championship titles in Career Mode. 

Win the 2.0L championship twice and you'll get a 'Level2' 
license which allows you to drive higher performance cars 
in the Single Race mode. 

Win the 2.0L championship four times in total and you'll 
get a 'Level3' license allowing you to drive at Performance 
Level 3 in Single Race mode.