I recently left a university that uses a Gmail interface for its email accounts and have subsequently lost access through the university's site. However I had synced the account with the Gmail app on my phone and can still access the account through it. Is there any way I can regain access to the account through the regular Gmail web application?
No, there isn't. We also use the Gmail interface (it's called G suite) for use within our organization.
FYI: they have to pay a monthly fee to keep your account on G suite as well.