The answer to your question might vary from state to state and insurance company to insurance company but with a new insurance policy only containing you on it, it is unlikely that any claims from your previous policy due to your ex-wife will affect your rates. When deciding to insure you, the new insurance company will be looking at your motor vehicle record, your claims history, and/or your insurance score. From your description they are clean, since you will be the only driver listed on the policy.

Some companies DO consider a husband/wife as a single entity (because of state laws) and in those cases her history may affect your rates.

The easiest way to find out is to shop for auto insurance and see what shows up under you as a single driver.

If insurance companies in your state do give you grief over past claims you can contact your state's insurance regulator to find out if and how long these claims could affect you since insurance company have to file their rates and rules with this regulatory body.