Yes, you can contribute to an HSA as long as you are covered by an HSA-qualified plan and have no disqualifying coverage such as Medicare or a full health FSA. It does not matter if the coverage is provided by an employer, through COBRA, or through individual insurance.   If you are covered for a partial year, you must pro-rate the max contribution for the number of months you were covered, but you have until tax day to complete your max contribution.   Finally, if a person is receiving insurance through COBRA or is receiving unemployment insurance, they may pay their health plan premiums with HSA funds tax-free, regardless of their age.