Your auto insurance score is effected by your credit score when you take out loans, credit cards etc.
So to improve your auto insurance score or keep the auto insurance score good then you should be responsible with credit and loans, pay bills on time, avoid applying for too many credit cards or loans which put hard inquiries on your credit report that lower your credit score.
Limiting the number of loans and credit cards in your name will also show that you're not a high risk for defaulting on loans or credit cards which help to improve your auto insurance score.