Assuming you signed-up for a non-HSA eligible plan with your new employer, your contributions will be limited based on a formula. Essentially you can only contribute a pro-rated amount of the annual maximum limit.
Here's the formula:
- Take the annual maximum contribution amount (in 2020 it's $3,550 for individual & $7,100 for family)
- Divide it by 12.
- Multiply that amount by the number of months you maintained HDHP coverage.
- That will be what you are allowed to contribute.
The same formula works for any catch-up contributions (catch-up contribution amount divided by 12, multiplied by # of months of HDHP coverage).
Source: IRS notice 2004-2 Q&A 2 through Q&A 7