Are newly licensed drivers covered by their parents insurance for a certain period of time until they can set up their own insurance?

You may need to get your insurance company to add the new driver on with a rider clause to be covered. It is possible that your coverage will allow the new driver, but, some insurance companies do not allow new drivers to be on the parents insurance, They make the new driver get an insurance policy on his or her license before they will cover them in the parents car. Check with your agent before you let the new driver operate the vehicle alone or you may loose your insurance.