Automatic coverage transfer from one vehicle to another may vary from insurance company to insurance company. Usually, you will be given thirty days of coverage to make the switch. Also, you will usually be given the same coverage that covered the old vehicle. Now, if this leased vehicle is 'totaled' in an accident and you had physical damage coverage with your previous vehicle, your insurance company will only pay up to the "actual cash value" of your old vehicle. To verify this, you will need to contact your insurance company.