Hair treatment that's bad, and not all the rage (5)
I believe the answer is:
singe
'hair treatment' is the definition.
(I've seen this in another clue)
'bad and not all the rage' is the wordplay.
I cannot really understand how this works, but
'bad' could be 'sin' and 'sin' is present in the answer.
The remaining letters 'ge' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
'that's' is the link.
Can you help me to learn more?
(Other definitions for singe that I've seen before include "Char, scorch" , "Scorch slightly on surface" , "slight burn" , "Result of match accident" , "Earnest entreaty" .)