Quietly and convincingly sacking commanding officer (6)
I believe the answer is:
gently
'quietly' is the definition.
(thesaurus)
'convincingly sacking commanding officer' is the wordplay.
'convincingly' becomes 'cogently' (I've seen this in another clue).
'sacking' indicates named letters should be taken away.
'commanding officer' becomes 'OC' (abbreviation for officer commanding).
'cogently' with 'oc' taken out is 'GENTLY'.
'and' acts as a link.
(Other definitions for gently that I've seen before include "Lightly, mildly, softly" , "Not violently" , "'Softly, kindly (6)'" , "In a mild/kind manner" , "in a peaceful manner?" .)