Quiet lieutenant accepts first-class braid (5)
I believe the answer is:
plait
'braid' is the definition.
(I know that braid can be written as plait)
'quiet lieutenant accepts first-class' is the wordplay.
'quiet' becomes 'p' (music symbol for 'piano', ie soft or quiet).
'lieutenant' becomes 'lt' (abbreviation for lieutenant).
'accepts' is an insertion indicator.
'first class' becomes 'ai' (A1 - top quality).
'lt' enclosing 'ai' is 'lait'.
'p'+'lait'='PLAIT'
(Other definitions for plait that I've seen before include "Braided pigtail" , "Weave hair" , "Intertwine" , "Stranded piece of hair" , "A rope of hair (5)" .)