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.
To be eligible to enroll in a Medicare Supplement plan, you must be enrolled in both Medicare Part A and Part B. A good time to enroll in a plan is generally during the Medigap Open Enrollment Period, which begins on the first day of the month that you are both age 65 or older and enrolled in Part B, and lasts for six months.