The Rule
Once you enroll in any part of Medicare (including no-premium Part A), you can't contribute to a Health Savings Account.
The Trap
Many 65-year-olds enroll in Part A "just because it has no premium" - and inadvertently disqualify themselves from HSA contributions, including any employer match.
The Optimization
If you're still working and contributing to an HSA, consider deferring Part A enrollment until you actually retire. You'll still get retroactive Part A coverage when you do enroll, up to 6 months back.
Catch
Social Security retirement benefits auto-enroll you in Part A. If you take Social Security at 65, you get Part A whether you want it or not. Plan accordingly.