Insurance normally follows a car first and driver second so yes, if you are loaning your car to another licensed driver in general your insurance as the car owner should cover him or her to drive since you gave the person permission to operate the vehicle. There are some insurance policies that have exclusions for other drivers, drivers under a certain age, etc so you would need to read through the terms of your policy and perhaps speak to an agent of your insurance provider to verify this other licensed driver would be covered by your policy while driving your car.
This extension of your coverage to a friend though is for him or her to borrow the car a few times here and there. If you loan your friend the car on a regular basis they will likely be required to be added to your policy as an occasional driver. If you are loaning your car to a friend for an extended period of time where they will keep the vehicle at their house and drive it daily then you would need to discuss this situation with your insurance company to see if it would be covered.
Some insurance companies would take issue with you covering a car that is no longer at your location but driven by someone else regularly and is garaged at a different location then your house. These change the risk factors involved in rating your policy for your vehicle.
Since insurance companies' guidelines vary you would need to see if they would continue coverage on the vehicle but require you to make changes, such as add the friend as a driver, or would not continue coverage on the vehicle and require your friend to obtain auto insurance of his own to cover the vehicle when he is operating it.
Most insurance companies require that you have insurable interest in a vehicle (have your name on the title or registration) in order to place insurance on a car however there are some, such as Esurance, that does allow someone to insure a car that they do not have insurable interest in.
If you plan on loaning your car to another licensed driver/friend you should contact your insurance carrier first and make certain that your policy covers the other person driving your car. Explain the situation whether it be just letting the person borrow the car occasionally or for an extensive amount of time so that your insurance agent can go over your company's guidelines and your policy terms to make sure your vehicle is properly covered and would pay out claims if the friend was in an accident in your car.
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