COBRA is continuation coverage after a job ends. It is not the same as current employer coverage. It generally does not let you delay Part B without a late-enrollment penalty. If you are turning 65, enroll in Part B on time unless you still have coverage from a current employer with 20 or more employees.

If you have both Medicare and COBRA, Medicare pays first on covered services. This is not a determination. Ask the COBRA administrator and Social Security.