Irrespective of deciding on COBRA or a retiree health plan, you should sign up for both Part A and Part B. Upon ceasing your work or when your coverage through your job concludes, there is an 8-month window for enrolling in Medicare (whichever is earlier). To avoid any interruption in your health coverage, it’s wise to get ahead by getting in touch with Social Security prior to the termination of your job’s insurance.
Neglecting to register for Part B within an 8-month timeframe after your existing job-related coverage ends could lead to a permanent late enrollment penalty. Additionally, your opportunity to sign up for Part B is limited to the Medicare General Enrollment Period (spanning from January 1 to March 31 each year), and you would only start receiving benefits starting in July. Consequently, this might cause a lapse in your health insurance.