Keep quiet about a son in the band (4)
I believe the answer is:
sash
'band' is the definition.
(sash is a kind of band)
'keep quiet about a son' is the wordplay.
'keep quiet' becomes 'sh'.
'about' is an insertion indicator.
'son' becomes 's'.
'a'+'s'='as'
'sh' going around 'as' is 'SASH'.
'in the' acts as a link.
(Other definitions for sash that I've seen before include "Framework to hold the panes of a window" , "Band worn over shoulder or round waist" , "Type of sliding window" , "(Uniform) strip; window-frame" , "Decorative band" .)