Do you already have the car? If so, contact the insurer as soon as possible. The grace period to add a newly purchased vehicle depends on company guidelines, the status of your policy, and if the car is a replacement or addition.
Does the new car replace a vehicle already listed on the policy? Replacement notification rules range from 4 - 30 days depending on the insurer. The new car will have the same coverages and limits as your trade-in. This could be a problem if you have liability-only insurance.
Perhaps the new car is an addition to your vehicle fleet. Another vehicle increases the insurance company's loss exposure. All insurers do not automatically extend coverage for this situation. Find out how your insurance company handles vehicle additions and verify reporting requirement beforehand.
There may be other insurance requirements depending if you paid cash or financed the new car. For example, physical damage (comprehensive and collision) is not state-mandated, but lenders generally insist on it. Or, the leasing company may recommend gap coverage.
Secure insurance coverage before driving off in the new car if your current auto policy is not in force.