So POST /students/{id}/enrollment

Or POST /students is the act of enrolling a student, so the returned Location might be /students/{id}/enrollment to reflect the current state of that resource.

The other details of the student might be at URLs like /students/{id}/details, /students/{id}/results, /students/{id}/courses etc etc

If I end up having part of a "sub-resource" in the "main" resource, then I try to always have an href, otherwise you have to put all of the information.

So GET /students/{id} might return a JSON object with an embedded "enrollment" object, but that embedded object would have an href to the full enrollment resource.