State laws differ however in most states there is not any grace period granted by law for you to obtain insurance after you have bought a new car. Most states require you to have insurance on a new vehicle before you operate it on public roadways.
When there are no state laws to guide insurance companies in regards to extending existing auto insurance coverage to a new car, insurers can have their own rules. So your car insurance company may by their own guidelines give a grace period to add your newly purchased car to your policy.
Generally speaking, many insurance carriers give you 30 days to get your new car registered and your title squared away and for you to inform them about your new vehicle. Some companies only offer this "grace period" for you to have coverage on your new car under your existing policy for only 14 days and some do not give you any grace period to place your car on your policy.
If your car insurance company does cover you for period of time after you purchase a car but before you have technically placed the car on your policy then normally you must be replacing a car already on the policy (say you traded in a car and replaced that car on your policy with the new car) and the coverages extended to you will be the same as the car you are taking off the policy.
In this scenario it would mean that if you traded in a car with only liability coverage than your new car would only have liability coverage on it during the grace period or if you had full coverage on the old vehicle than your new vehicle should also be extended to the new vehicle if your insurer offers a grace period in which to put your new vehicle on your current insurance policy.
Since insurance companies' policy guidelines vary in if a new car will have any grace period to be placed on your policy it is best to discuss this issue with your insurance carrier before buying a new car. Even if there is a "grace period" it is always best to inform your insurance agent when you have purchased a new car and to give him the information needed to get the motor vehicle properly placed on the policy as soon as possible after your purchase of it.
To find out what your state's laws are regarding grace periods to add a newly purchased car to your policy, check with your state insurance regulatory body. Then to find out if your current car insurance policy would extend to a new car that you buy for a certain amount of time (grace period) speak to your agent.