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.
Generally, your Initial Enrollment Period for Part D will occur at the same time as your Initial Enrollment Period for Medicare Part B (the seven-month period that starts three months before your eligibility for Part B, includes the month you are eligible, and ends three months later).