Cutting remark made by hairdresser without hesitation (4)
I believe the answer is:
Here is my best explanation:
'cutting remark' is the definition.
(I've seen this before)
'hairdresser without hesitation' is the subsidiary indication.
'hairdresser' becomes 'barber' (barber is a kind of hairdresser).
'without' indicates named letters should be taken away.
'hesitation' becomes 'er'.
'barber' with 'er' taken out is 'barb'.
'made by' is the link.
(Other definitions for barb that I've seen before include "Stage whispers", "Pointed remark", "Kind of thorn or wounding remark", "Gibe", "Backward-facing part of hook", "Slight", "added to wire?", "Backward-pointing part of a fish hook", "Spike" and "Hurtful comment".)