Yes. To be eligible to open and contribute to an HSA, you need to be enrolled in a qualified high-deductible health plan (HDHP), per the U.S. Internal Revenue Service. Enrollment in the university’s Healthy Savings Plan qualifies you for an HSA, as long as you also meet the other eligibility requirements, which are specified on the HSA webpage.
You may keep an old HSA with contributions from previous years--including an HSA from a previous employer or from previous years with the university--even if you are not enrolled in a high-deductible health plan. But if you are not currently enrolled in an IRS-approved HDHP, you may not contribute to the old HSA, and you may be charged an administration fee.