Generally speaking, getting a separate car insurance policy for your teen son isn’t going to save you money. If anything, it will likely cost you money.
Your son can expect to be charged much higher rates for his own insurance because of his young age and lack of driving experience; his lack of established credit; and his lack of continuous insurance coverage.
Furthermore, if he has his own policy, your son won’t have access to discounts for insuring multiple vehicles or multiple drivers, for example.
So having said all that, I highly recommend adding your son to your existing policy. This will raise your rates, but it will be cheaper than getting a standalone policy for your son.