Short answer: No. Once you enroll in any part of Medicare, including premium-free Part A, you can no longer contribute to an HSA, though you can still spend the existing balance. To keep contributing while working past 65, you must delay all of Medicare, which usually means not claiming Social Security.
Enrolling in any part of Medicare makes you ineligible to contribute to an HSA (spending the balance is always fine). This trips up people who take premium-free Part A at 65 out of habit.
If you’re working past 65 with qualifying coverage and want to keep funding your HSA, you must delay all of Medicare, and note that claiming Social Security automatically enrolls you in Part A, so you generally can’t be on Social Security either. Also watch the 6-month retroactive Part A trap: when you do enroll, Part A can backdate up to six months, so stop HSA contributions ahead of time to avoid an excess contribution. The 2025 One Big Beautiful Bill did not change this rule.