Promise quiet entertaining Cambridge University author (9)
I believe the answer is:
wordsmith
'author' is the definition.
(wordsmith is a kind of author)
'promise quiet entertaining cambridge university' is the wordplay.
'promise' becomes 'word' (as in 'I give you my word').
'quiet' becomes 'sh'.
'entertaining' indicates putting letters inside.
'cambridge university' becomes 'mit' (Massachusetts Institute of Technology in Cambridge).
'sh' going around 'mit' is 'smith'.
'word'+'smith'='WORDSMITH'
(Other definitions for wordsmith that I've seen before include "Person skilled at writing" , "he'd be good at coining?" , "fluent writer" , "Author" , "Skilled writer or orator" .)