Take for granted quietly missing 'Carry On' (6)
I believe the answer is:
resume
'carry on' is the definition.
(I've seen this before)
'take for granted quietly missing' is the wordplay.
'take for granted' becomes 'presume' (to take for granted as true).
'quietly' becomes 'p' (p for piano and quiet).
'missing' is a deletion indicator.
'presume' with 'p' removed is 'RESUME'.
(Other definitions for resume that I've seen before include "list of achievements in Washington?" , "Continue after a break" , "account, in brief" , "Pick up again" , "proceed" .)