The most common and most likely answer to this crossword clue is the 6 letter word OUTWIT
I've seen this crossword clue in The Guardian
O
U
T
W
I
T
More clues leading to the result OUTWIT
- Be cleverer than foolish undergraduate?
- Get the better of idiot from Open University?
- Get the better of idiot joining higher education establishment
- Revealed card is better
- Get the better of berk at Balliol?
- Wife, not in normal position, coming first given sex trick
- Cunningly defeat without being heartless, having switched halves
- Fox, duck, cougar’s third, then ass
- Get the better of the fool among us? That’s not right
- Be too clever for Oxford University idiot
Buddy explains!

The straight part
We know that "Cunningly defeat" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cunningly defeat = outwit.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does OUTWIT mean?
OUTWIT verb- To get the better of; to outsmart, to beat in a competition of wits.