Finally recognised compere of University Challenge (4)
I believe the answer is:
defy
'challenge' is the definition.
(defying is a kind of challenging)
'finally recognised compere of university' is the wordplay.
'finally' suggests the final letters.
The final letters of 'recognised compere of university' are 'DEFY'.
(Other definitions for defy that I've seen before include "Resist (someone) openly" , "Go against (authority)" , "Withstand" , "Openly resist or refuse to obey" , "Stand against" .)