Do I need insurance once we start practice driving for my new driver?
No. They are covered under the insurance policy of whomever they are driving with until they get their license. The day they get their license they will need to make the call and have their own insurance put in place. New Hampshire does not legally require insurance of financially responsible drivers, (Live Free or Die,) but any responsible driver will want to have good insurance. Make those calls, look into pricing. Usually it is least expensive to add your new driver onto an existing policy, but it absolutely worth shopping around. No insurance company will mind giving you an estimate.