Ablest two fit to engage in intellectual competition (6,2,4)
I believe the answer is:
battle of wits
'intellectual competition' is the definition.
(a battle or contest of the mind)
'ablest two fit to engage' is the wordplay.
'to engage' indicates an anagram (letters engaged or used in a different way).
'ablest'+'two'+'fit'='ablesttwofit'
'ablesttwofit' is an anagram of 'BATTLE OF WITS'.
'in' acts as a link.
(Other definitions for battle of wits that I've seen before include "Mental duel" , "Intelligent rivalry" .)