A medical college starting to become famous (9)
I believe the answer is:
acclaimed
'famous' is the definition.
(thesaurus)
'a medical college starting to become' is the wordplay.
'starting' suggests taking the first letters.
'to become' indicates an anagram.
The initial letter of 'college' is 'c'.
'medical'+'c'='medicalc'
'medicalc' is an anagram of 'cclaimed'.
'a'+'cclaimed'='ACCLAIMED'
(Other definitions for acclaimed that I've seen before include "Strongly praised" , "Hailed, heralded" , "Highly respected" .)