Frank, not entirely quiet, becoming cheeky (5)
I believe the answer is:
fresh
'cheeky' is the definition.
(I've seen this before)
'frank not entirely quiet' is the wordplay.
'frank' becomes 'free' (I've seen this in other clues).
'not entirely' means to remove the last letter.
'quiet' becomes 'sh'.
'free' with its last letter removed is 'fre'.
'fre'+'sh'='FRESH'
'becoming' is the link.
(Other definitions for fresh that I've seen before include "Newly-made" , "Recently made, produced, or harvested" , "Informally impudent, not stale" , "New-fangled" , "Recently picked" .)