Stylish Post Office shut up (4)
I believe the answer is:
posh
'stylish' is the definition.
('posh' can be similar in meaning to 'stylish')
'post office shut up' is the wordplay.
'post office' becomes 'po'.
'shut up' becomes 'sh'.
'po'+'sh'='POSH'
(Other definitions for posh that I've seen before include "Upper-class; stylish" , "Mrs 4 across (colloq.)" , "Swanky" , "Smart - upper-class" , "Elegant and fashionable" .)