No. Medicare Supplement, also known as Medigap, plans have no enrollment period. However if you are currently enrolled in a Medicare Advantage plan, you will have to wait for one of the times you can unenroll before you can enroll in the Medigap plan.
There are some times that are better to enroll in a Medigap plan. When you are both 65 and newly enrolled in Medicare part B, you have a period of time when you can pick any plan regardless of your health conditions. In some states, you're allowed to change plans during the month of your birthday.
When you first enroll in Medicare Part B at age 65 or older you will be in your initial Medicare Open Enrollment Period to purchase a Medicare Supplement. You have six month from when your Part B takes effect to enroll in a Medicare Supplement without having to answer any health questions. Your acceptance is guaranteed and pre-existing health conditions are covered immediately with no waiting period. You can purchase a Medicare Supplement anytime you want to outside of your initial Open Enrollment Period but once your Open Enrollment Period ends you will have to answer all health questions to qualify for a Medicare Supplement. If you have a serious health condition you could be denied coverage or have to pay a much higher premium to get the pre-existing health condition covered.
There are some times that are better to enroll in a Medigap plan. When you are both 65 and newly enrolled in Medicare part B, you have a period of time when you can pick any plan regardless of your health conditions. In some states, you're allowed to change plans during the month of your birthday.