All you'll need to unlock the higher tier licenses is a ton of Sega Miles. You'll get Sega Miles at the end of a race whether you win or lose, but winning gives you more. The mile requirements are for total miles earned, so you can spend your miles without worrying about making the next license harder to get.
The license ranks are:
- Blue - 50,000 miles
- Amber - 100,000 miles
- Red - 150,000 miles
- Bronze - 300,000 miles
- Silver - 500,000 miles
- Gold - 750,000 miles
As getting these licenses are trophies/achievements, most of this info comes from the PS3Trophies page for this game.