Quietly shelves promises (7)
I believe the answer is:
pledges
'promises' is the definition.
(pledge is a kind of promise)
'quietly shelves' is the wordplay.
'quietly' becomes 'p' (p for piano and quiet).
'shelves' becomes 'ledges' ('ledge' can be a synonym of 'shelf').
'p'+'ledges'='PLEDGES'
(Other definitions for pledges that I've seen before include "Promises" , "Vows" , "Loyal toasts" .)