If it is more than 6 months since you turned 65, Medicare will become effective on the first day of the month that is 6 months before you applied. So if you apply December 1, Medicare should be retroactive to June 1. That means you had 5 months of HSA eligibility for 2024, and your contribution limit would be 5/12th of $4150 (if covered by a single HDHP) or 5/12th of $8300 (if covered by a family HDHP) plus 5/12 of $1000 as your catch-up provision.
However, if you just turned 65, Medicare will not necessarily be 6 months retroactive. If it is 3 months before your 65th birthday, to 6 months after your 65th birthday, Medicare will be activated on the 1st day of the month in which you turned 65.
Assuming Medicare is effective June 1, your limit for 2024 would be $3875. You will need to remove the excess contributions no later than April 15, 2025. This is a special procedure, not a regular withdrawal , so contact the HSA bank first.
If you are married, your spouse may have options to keep contributing to a separate account in her name, if she is covered by an HDHP, even is the plan belonged to you.
