Keep quiet about a son in 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' means one lot of letters goes inside another.
'son' becomes 's'.
'a'+'s'='as'
'sh' placed around 'as' is 'SASH'.
'in' is the link.
(Other definitions for sash that I've seen before include "Baldrick" , "Decorative belt" , "Framework to hold the panes of a window" , "Band - scarf" , "Sliding window frame" .)