You may have a grace period (typically 7 to 30 days) where your current policy automatically extends to a new purchase. However, this is not a guarantee and may only provide the same level of coverage as your old car—which might not be enough for a brand-new vehicle.
If you want to avoid being rushed at the dealership, choose your insurer in advance. Have their contact info ready so you only have to provide the final VIN to "bind" the coverage. do you buy insurance before or after the car
Are you planning to your vehicle, or will this be a cash purchase ? You may have a grace period (typically 7