The education required to become a state trooper varies by state, but in general at least a year of post-high school education is required. In some states, if you have served in the military the post-high school educational requirement is waived because of your experience.
You can enroll in Medicare Part D coverage once you meet both of the above requirements. Your Initial Enrollment Period for Part D is when you're first eligible to sign up for prescription drug benefits, and this period usually coincides with when you're first eligible for Medicare coverage.
When you turn 65 (and have no other drug coverage that is as good as Medicare), you need to join a Part D drug plan during the 7-month initial enrollment period when you can sign up for Medicare Part A and Part B. This period runs from three months before the month of your 65th birthday to three months after it.