Scotsman enters Post Office quietly (5)
I believe the answer is:
piano
'quietly' is the definition.
(synonyms)
'scotsman enters post office' is the wordplay.
'scotsman' becomes 'ian' (common Scottish name).
'enters' is an insertion indicator.
'post office' becomes 'po' (abbreviation).
'ian' going inside 'po' is 'PIANO'.
(Other definitions for piano that I've seen before include "Soft, softly (music)" , "Quiet (music)" , "soft passage" , "Stringed instrument - to be played quietly" , "Softly, musically speaking" .)