Receive a degree from what could become rated a good university, initially (8)
I believe the answer is:
graduate
'receive a degree' is the definition.
(I've seen this before)
'what could become rated a good university initially' is the wordplay.
'what could become' indicates anagramming the letters.
'initially' suggests taking the first letters.
The initial letters of 'good university' is 'gu'.
'rated'+'a'+'gu'='ratedagu'
'ratedagu' is an anagram of 'GRADUATE'.
'from' is the link.
(Other definitions for graduate that I've seen before include "Obtain a degree - one with a degree" , "Recipient of degree" , "Successfully complete a course in higher education" , "Person holding university degree" , "University type" .)