Keep quiet over book (8)
I believe the answer is:
preserve
'keep' is the definition.
(preserving is a kind of keeping)
'quiet over book' is the wordplay.
'quiet over' becomes 'p' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'book' becomes 'reserve' ('reserve' can be a synonym of 'book').
'p'+'reserve'='PRESERVE'
Can you help me to learn more?
(Other definitions for preserve that I've seen before include "put on the table in advance?" , "Keep (something) safe" , "Particular interest" , "Jam or marmalade" , "area where game is held" .)