Quiet chap in post office (5)
I believe the answer is:
piano
'quiet' is the definition.
(I've seen this before)
'chap in post office' is the wordplay.
'chap' becomes 'ian' (man's name).
'in' is an insertion indicator.
'post office' becomes 'po' (abbreviation).
'ian' inserted inside 'po' is 'PIANO'.
(Other definitions for piano that I've seen before include "Opposite of forte" , "Softly (mus.)" , "one of 6 [STEINWAYS]" , "Softly, musically speaking" , "Musical instrument - softly, please" .)