You can establish an HSA on the first day of the month that you have a qualified HDHP and are otherwise an eligible individual. You lose eligibility to establish or contribute to an HSA if you become covered by a health plan other than an HDHP, become enrolled in Medicare, or become a dependent on another individual’s tax return.
Although an existing HSA can be used on a tax-preferred basis for qualified medical expenses, you cannot contribute to the HSA or establish other HSAs unless you become an eligible individual again.