Cutting remark from hairdresser with no sign of hesitation (4)
I believe the answer is:
barb
'cutting remark' is the definition.
(as in a barbed comment)
'hairdresser with no sign of hesitation' is the wordplay.
'hairdresser' becomes 'barber' (barber is a kind of hairdresser).
'with no' suggests deleting specific letters.
'sign of hesitation' becomes 'er'.
'barber' with 'er' taken out is 'BARB'.
'from' acts as a link.
(Other definitions for barb that I've seen before include "Twisted point of hook" , "Backward-facing part of hook" , "Stage whispers" , "Aggressive remark intended to have a telling effect" , "Part of an arrow head" .)