Though you can no longer contribute to an Health Savings Account (HSA) after you sign up for Medicare, you can use any funds previously placed in an HSA account to pay tax-free for any portion of medical expenses you incur while on Medicare. In fact, you can use the money for anything after age 65, although you will pay taxes if you make any withdrawals for non-medical expenses.
However, there are many medical expenses not covered by Medicare which you can use HSA funds to pay. For example, you can money in your HSA account to pay Medicare deductibles and co-payments, as well as premiums for Medicare parts A, B and D (prescription-drug coverage), as well as Medicare Advantage premiums and qualified long-term-care premiums. However, one thing you can not use HSA funds to pay tax-free is a Medigap or Medicare Supplement plans.