Yes, you may either keep using the debit card that you have until you have spent all of your HSA funds or you may go onto the PayFlex website stateoftn.payflexdirect.com, scroll to the bottom of the page and under Forms > Health Savings Account Forms, fill out the HSA Trustee Transfer Form. Send that to PayFlex if you are going to another employer who offers a HSA. This will allow you to have the funds in your HSA transferred directly to your HSA with your new employer.
If you keep your HSA through the state-sponsored plan and continue to use your debit card, then the monthly administrative fee that the state has been paying will be your responsibility and that monthly fee will be taken directly out of your HSA each month. If your HSA balance draws down to zero and you are not an active enrollee, your HSA will be automatically closed.