Trivial broadcast about country house (7)
I believe the answer is:
shallow
'trivial' is the definition.
(thesaurus)
'broadcast about country house' is the wordplay.
'broadcast' becomes 'sow' (sowing is a kind of broadcasting).
'about' is an insertion indicator.
'country house' becomes 'hall'.
'sow' placed around 'hall' is 'SHALLOW'.
(Other definitions for shallow that I've seen before include "Not profound" , "Without depth" , "Of water, not deep" , "Superficial" , "Of no great depth" .)