Wary about being wrong (4)
I believe the answer is:
'being wrong' is the definition.
('awry' can be a synonym of 'wrong')
'wary about' is the wordplay.
'about' indicates anagramming the letters.
'wary' is an anagram of 'AWRY'.
(Other definitions for awry that I've seen before include "Distorted, crooked" , "Wary but distorted." , "Out of kilter" , "(Gone) askew" , "the wrong direction" .)