Broadcast Scrapheap Challenge's final run across country (5,5)
I believe the answer is:
paper chase
'run across country' is the definition.
(a paper chase is a cross-country race)
'broadcast scrapheap challenge's final' is the wordplay.
'broadcast' indicates an anagram (letters scattered or cast around).
'final' suggests the final letters.
The final letter of 'challenge' is 'e'.
'scrapheap' anagrammed gives 'paperchas'.
'paperchas'+'e'='PAPER-CHASE'
(Other definitions for paper chase that I've seen before include "Cross-country race following trail" , "Type of cross-country race" , "cross country run" , "Trail-following cross-country race" .)