I switched from the disc edition to digital long time ago. You need to delete the (disc) client and purchase the ARR starter edition at ps-store. All Expansions and CE's you already own will still be available after installing the digital ed.
After getting a new edition, you will also be prompted to make a new FFXIV service account which you probably won't need anyway. Use the old one after finishing the setup.
(at the library, clients which require a disc will have label showing a disc)