In that broadcast conflict comes across (7)
I believe the answer is:
athwart
'across' is the definition.
(athwart can mean across or over)
'in that broadcast conflict' is the wordplay.
'in' means one lot of letters goes inside another.
'broadcast' is an anagram indicator (letters scattered or cast around).
'conflict' becomes 'war' (war is a kind of conflict).
'that' anagrammed gives 'atht'.
'atht' going around 'war' is 'ATHWART'.
'comes' is the link.
(Other definitions for athwart that I've seen before include "wrongly" , "Transverse; at an oblique angle" , "What rat is placed across?" , "Crossing" , "Crosswise" .)