The Medigap Open Enrollment Period is a one-time 6-month period. This time frame begins the first month of your Medicare Part B coverage, and you’re 65 or older. Some states may have additional Open Enrollment rights under state law. If you apply for a Medigap plan during this time, you are guaranteed acceptance and the plan can’t charge more based on your health conditions. To enroll in a Medigap plan, you must first be enrolled in Medicare Part A and Part B.