Keep quiet with book (8)
I believe the answer is:
preserve
'keep' is the definition.
(I know that keep can be written as preserve)
'quiet with book' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'with' means one lot of letters go next to another.
'book' becomes 'reserve' (as in booking or reserving in advance).
'p'+'reserve'='PRESERVE'
(Other definitions for preserve that I've seen before include "Keep safe from spoilage" , "Refuse to give up" , "Keep alive; jam" , "Maintain - jam" , "Keep alive, maintain" .)