Does an employee with existing group health insurance have to enroll into Medicare at age 65 buy a supplemental plan then drop the group health insurance?

You have a choice to stay in your employer's plan or join Medicare. When you do stop working and lose your group health plan, make sure you enroll in Medicare within 8 months.

You could also enroll in Medicare Part A (hospital coverage), and postpone enrolling in Part B (physician coverage) until you are done with your group health plan. Part A does not cost you a monthly premium. You would be over-insured, but the Part A benefit is available to you at age 65, whether you have other coverage or not.