If the child either lives in the household or lists their parent's house as their permanent residence while at college then usually an insurance company will require the child to remain on the parent's insurance policy.
If the child remains in the parent’s household after college then he or she would need to continue to be listed as a driver on the policy as well.
Most insurance companies will require you to continue to have your licensed child listed on your auto insurance policy as long as they live in your household, even if they are 18 or older in age. Usually your insurance carrier will want all licensed drivers dwelling in a residence listed on the policy.
To find out what your insurance company mandates, since insurance companies guidelines can differ, contact your insurance agent. To find out if there are any specific state insurance laws governing this situation you can contact your state's insurance regulator.