Will insurance cover an accident by an unlicensed driving a licensed insured drivers car?

It just depends on the type of insurance policy that was in force on the car and whether the unlicensed driver is considered an insured under the terms of the Vehicle owners Auto Insurance Policy.

If the Vehicle Owner has a "Standard Form Policy" then in most cases where there is no violation of law, fraud, or deception, a permissive use driver would be covered under the owners policy.

If the Vehicle Owner has a "Named Driver Policy", Often referred to as a "Limited Lines Policy" available as a more economic option in some states. Then no drivers other than those listed on the policy are covered.

It's best just to contact your agent or your insurer to determine the extent of coverage provided under your auto insurance policy.

If on a standard form policy and the accident is covered, you may be surcharged an additional premium or suffer policy cancellation for the negligent action of allowing an unlicensed driver to operate the vehicle

Answer

Generally, if they cover the loss, it would be the insured's driver's car insurance. This question really is to general and really requires specific policy review.