If the driver of your car was at-fault for the accident (wholly or partially) then it is likely that your auto insurance premium will increase.
Car insurance is tied to the vehicle and not the person. If you lend your car out to a friend or family member and your vehicle is involved in an accident it will be the policy covering the vehicle that will be affected. Remember, if you lend your car, you are in essence lending your car insurance.
That said, if you lend your car and the driver gets a speeding ticket, the ticket is their problem--not yours--in the insurance world.