There are 7 leagues in total. These are, from the highest to lowest:
After each race season ends, the 3 clubs with the highest scores goes to the higher league (if you're already in the highest league, you stay there) and gets the best rewards available. The 3 clubs with the lowest scores (if you're already in the lowest league, you stay there) don't get rewards and goes to the lower league.
If you're not one of the first 3 or last 3 clubs, you stay in the same league.