Book full of promise about Cochran's style of music? (8,4)
I believe the answer is:
brighton rock
'book' is the definition.
(I've seen this before)
'full of promise about cochran's style of music?' is the wordplay.
'full of promise' becomes 'bright' (I've seen this before).
'about' becomes 'on'.
'cochran's style of music?' becomes 'rock' (Eddie Cochran was a rock musician).
'bright'+'on'+'rock'='BRIGHTON ROCK'
(Other definitions for brighton rock that I've seen before include "... hard cylindrical sweet from the seaside" , "Film" , "Hard tubular sweet from East Sussex" , "Work of fiction" , "What offers colourful writing all through" .)