Yes. If you have a health savings account (HSA), your contribution to a self-only plan is permissible up to set annual limits (in 2019 it’s $3,500, plus $1,000 if you’re age 55 or older by year end). Alternatively, if you have a dependent under the HDHP, you can contribute to an HSA up to the limit for family coverage.
A 12-month period ending on the last day of any month other than December. Partnerships, S corporations, and personal service corporations are limited in their choice of fiscal years and face special restrictions.