It depends on how you purchased your vehicle. If you were financing your vehicle, I do not believe you will receive any refund. It is usually part of your vehicle's financed monthly payment. The coverage that gets paid for (monthly) is used that same month, even if you did not have to make a claim against it.
If you paid for your vehicle and your gap insurance policy up front in full, you will need to contact the company you purchased the policy through to see if there is any unused premium which needs to be refunded back to you.
If your insurance rates increase when you trade-in your vehicle, you can come here to find auto insurance quotes for new vehicles.