A close shave is wrong (5)
I believe the answer is:
amiss
'is wrong' is the definition.
(synonyms)
'a close shave' is the wordplay.
'close shave' becomes 'miss' (I am not sure about this - if you are sure you should believe this answer much more).
'a'+'miss'='AMISS'
Can you help me to learn more?
(Other definitions for amiss that I've seen before include "Wrong (a girl!)" , "Haywire" , "Not quite right" , "error" , "Wrong; inaccurate" .)