Cutting remark made by hairdresser without hesitation (4)
I believe the answer is:
barb
'cutting remark' is the definition.
(I've seen this before)
'hairdresser without hesitation' is the wordplay.
'hairdresser' becomes 'barber' (barber is a kind of hairdresser).
'without' is a deletion indicator.
'hesitation' becomes 'er'.
'barber' with 'er' taken away is 'BARB'.
'made by' is the link.
(Other definitions for barb that I've seen before include "Backward-pointing part of a fish hook" , "Deliberately hurtful remark" , "Cruel remark" , "Point of fish-hook - gibe" , "Sharp spike pointing backward" .)