Assuming you signed-up for a non-HDHP 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. You will take the annual maximum contribution amount and divide it by 12. Then 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 7Updated: