Your Gap insurance may be voided if you refinance since the terms and guidelines for gap insurance can vary depending upon the insurance company that the insurance is written with. It would depend upon the terms of your Gap insurance as well as to if you purchased through your current lender or elsewhere. However, typically, your Gap insurance will be cancelled out if you refinance.
To find out for certain if your gap insurance will be affected by refinancing your vehicle with another lender contact your GAP insurance provider and read through the terms of your current policy.
If you know after the refinancing of your vehicle that you owe more than its actual cash value (ACV) then Gap insurance could be beneficial for you to purchase again for your new refinanced loan.