Challenge: some demand a recount (4)
I believe the answer is:
dare
'challenge' is the definition.
(daring is a kind of challenging)
'some demand a recount' is the wordplay.
'some' indicates the answer is hidden within the clue (some of the parts of the word are used).
'DARE' can be found hidden inside 'demand a recount'.
(Other definitions for dare that I've seen before include "Throw down the gauntlet" , "Dan - - , 'Eagle' pilot" , "Be courageous enough to try or do" , "Venture, have courage" , "Challenge to do something dangerous" .)