Page starts to rally some university bigwigs (7)
I believe the answer is:
rectors
'university bigwigs' is the definition.
'page starts to rally some' is the wordplay.
'page' becomes 'recto' (recto is a kind of page).
'starts to' indicates taking the first letters.
The first letters of 'rally some' is 'rs'.
'recto'+'rs'='RECTORS'
(Other definitions for rectors that I've seen before include "Clergymen" , "ministers" .)