Medigap or Medicare Supplement coverage applications aren’t accepted during Medicare’s annual open enrollment period (October 15 – December 7). If you are 65 or older and enrolled in Medicare Part B, you are eligible to sign up for Medigap coverage during the six-month enrollment period that begins on the first day of the month in which you turn 65. A Medigap policy may be harder to come by and more expensive once this period has passed. Various states have different procedures, but there are supplemental open enrollment windows in some circumstances.