Family broadcaster's screening with artist (9)
I believe the answer is:
kandinsky
'artist' is the definition.
(I've seen this before)
'family broadcaster's screening with' is the wordplay.
'family' becomes 'kin' ('kin' can be a synonym of 'family').
'broadcaster' becomes 'sky' (I've seen this before).
'screening' is an insertion indicator (I've seen this in other clues).
'with' becomes 'and' (I've seen this before**).
'kin'+'sky'='kinsky'
'kinsky' placed around 'and' is 'KANDINSKY'.
(Other definitions for kandinsky that I've seen before include "Artist" , "Wassily --, painter born in Moscow" .)