You are ineligible to make deposits into an HSA if you are enrolled in Medicare. Deposits can only be made to an HSA when you are covered by a high-deductible health plan (HDHP) and are below the age of 65. Upon reaching age 65 or enrolling in Medicare, you are no longer able to make deposits into the HSA.
As the HSA owner, your employer does not control the account, and you have the ability to contribute until you reach age 65. The funds in the HSA may be utilized for eligible medical expenditures, irrespective of your current Medicare enrollment status.
On reaching age 65, you gain greater leeway in utilizing the funds from your HSA. Nevertheless, at this stage, additional contributions to the HSA are not permitted.