Starting a new job on Dec 13; had FSA at previous employer; can I sign up for HDHP and contribute to HSA for the rest of 2021?

Can someone please provide some clarification on whether I will be able to elect an HDHP at my new job and if I can contribute to an HSA for the remainder of the year if I start my new job on Dec 13, 2021?  If so, is there a maximum amount that I can contribute?  I had an all purpose FSA at my previous employer and I've used up the funds.