At his wits' end, a chap looks happy! (6)
I believe the answer is:
smiles
'looks happy' is the definition.
(someone smiles when they are happy)
'at his wits' end a chap' is the wordplay.
I cannot really see how this works, but
'chap' could be 'miles' and 'miles' is present in the answer.
A single letter 's' remains which might be clued in a way I don't understand.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for smiles that I've seen before include "Shows signs of pleasure or amusement" , "Gives visible sign of pleasure" , "Beams, grins" , "Looks happy" , "Facial expressions showing pleasure" .)