Grand arena houses challenge (4)
I believe the answer is:
dare
'challenge' is the definition.
(I know that dare is a type of challenge)
'grand arena houses' is the wordplay.
'houses' says the answer is hidden in the clue (part of the clue houses the answer).
'DARE' can be found hidden inside 'grand arena'.
(Other definitions for dare that I've seen before include "Have sufficient courage" , "Challenge of courage" , "Be courageous enough to try or do" , "Dan - - , 'Eagle' pilot" , "Venture to read" .)