What's the meaning of "vicemaster of a Cambridge college"?

Question

I know the meaning of vicemaster but I didn't know if the "vicemaster of a Cambridge college" means "vicemaster of one of the Cambridge colleges" or means "vicemaster of the whole of Cambridge university"?

The text is here:

The first week passed in a blur of lectures. In the second week, every student was assigned a supervisor to guide their research. My supervisor, I learned, was the eminent Professor Jonathan Steinberg, a former vicemaster of a Cambridge college, who was much celebrated for his writings on the Holocaust.

Answer 1

This is not really about "English", but about the structure of Cambridge University.

Cambridge University is made up of multiple "colleges" each of which is fairly independent. The University itself is run by a "Vice-Chancellor" (the chancellor being an honorary post). Each college is run by a Master, who is assisted by a vice-master.

The grammar of the sentence makes this clear "of a Cambridge college" = "of one of the Cambridge colleges".

Answer 2

According to Cambridge Dictionary (what a coincidence! No irony)

college noun (EDUCATION)

1. (us) a university where you can study for an undergraduate (= first) degree

2. one of the separate and named parts into which some universities are divided:

   King's College, Cambridge

Apart from 2., the determiner a let us infer that there are more than one college in that university.