Medicare eligibility begins the month of your 65th birthday or within the three months afterward. It’s best to apply for coverage as soon as possible, as delays may occur if you do. You could sign up for an Advantage Medicare plan during the yearly open enrollment period even if you missed your chance when you turned 65. Each year, you can change from traditional Medicare to Medicare Advantage from October 15th to December 7th. You can add, drop, or alter your Part D coverage and change Medicare Advantage plans.