ISO 9001 is about demonstrating the ability to consistently provide products and services that meet customer and regulatory requirements. So, ISO 9001 can help align an organization around a policy, a set of priorities, translated into objectives. And a management system is about working to meet those objectives. So, for each area, teaching, research, ... Who are the critical interested parties? What do they need and expect? How can the university organize itself in order to be focused on delivering those outcomes?
ISO published in 2003, IWA 2:2003 - Quality management systems - Guidelines for the application of ISO 9001:2000 in education, a document updated in 2007 by IWA 2:2007 - Quality management systems -- Guidelines for the application of ISO 9001:2000 in education. However, as far as I know, this 2007 guideline has been withdrawn.
ISO published in 2018, ISO 21001:2018 - Educational organizations -- Management systems for educational organizations -- Requirements with guidance for use. ISO 21001:2018 is a management system standard that is partially aligned with ISO 9001:2015 for quality management systems.
The following material will provide you information about a QMS in an education setting: