First of all, if you are also over age 55, your overall contribution limit is $9100, by using a special provision:
First, remember that an HSA belongs to one person, it is never a "joint" account. If your spouse has a family HDHP and is HSA-eligible, then you are also considered to have a family HDHP and can contribute to an HSA in your own name. (You may have to open one at a private bank if your employer does not offer one.) If you are over age 55, you can contribute the $1000 catch-up provision to an account in your name. Your overall family limit (ignoring Medicare) is $9100, where the $7100 general limit can be split between the 2 of you, but each $1000 catch-up contribution can only be contributed to an account in your own names.
Now to add in Medicare: Eligibility for HSA contributions is determined on the first day of the month. However, Medicare is backdated to the first day of the month in which the person turns 65, even if you enroll late.
If you sign up for Medicare Part A (Hospital Insurance) and/or Medicare Part B (Medical Insurance) during the first 3 months of your Initial Enrollment Period, your coverage starts the first day of the month you turn 65. If your birthday is on the first day of the month, your coverage starts the first day of the prior month.
Therefore, your spouse is not eligible to contribute for December. Her contribution limit for 2020 is $7425. This is per the worksheet on page 4 of the form 8889 instructions. https://www.irs.gov/pub/irs-pdf/i8889.pdf
However, if you are covered by her family HDHP and you have not turned 65, your contribution limit for the year is your full amount of $8100 ($7100 family limit plus $1000 individual catch-up, as I explained earlier.) So if your wife contributes $7425 through her employer, you can contribute an additional $1591 to your own HSA. (One month of family limit at $591 and your personal catch-up provision of $1000).
To break it down, your wife's limit for 2020 will be ($7100 x 11/12 plus $1000 x 11/12) but your personal limit will be $7100 plus $1000. Therefore, if your wife contributes $6508 plus $916, you can contribute $592 plus $1000.
And if you continue to be covered under her HDHP in 2021, you can continue to make deductible contributions to an HSA in your own name, even though she is ineligible to make contributions under her name.
