Fed up with conclusion to University Challenge (4)
I believe the answer is:
defy
'challenge' is the definition.
(defying is a kind of challenging)
'fed up with conclusion to university' is the wordplay.
'up with' indicates an anagram (letters get chucked up).
'conclusion to' indicates one should take the final letters.
The last letter of 'university' is 'y'.
'fed' mixed up with 'y' can make 'DEFY'.
(Other definitions for defy that I've seen before include "Disobey boldly and openly" , "Withstand" , "Openly resist or refuse to obey" , "Flout" , "Stand against" .)