Yes, you can apply for Medicare Aid if you have private Medi-gap insurance. However, you cannot receive both benefits at the same time. If you are approved for Medicare Aid, your Medi-gap insurance will be suspended for up to 24 months. This means you can resume your Medi-gap insurance policy during that 24 months if your Medicare Aid benefits stop. After 24 months if your Medicare-Aid benefits stop, you must reapply for Medi-gap insurance. You are not guaranteed to be approved.