... unique hairdressers, maybe with first cut conclusively free (5)
I believe the answer is:
alone
'unique' is the definition.
(I've seen this in another clue)
'first cut conclusively free' is the wordplay.
'first' becomes 'a' (first letter of the alphabet).
'cut' becomes 'lon' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'conclusively' says to take the final letters (the letter which concludes the word).
The final letter of 'free' is 'e'.
'a'+'lon'+'e'='ALONE'
'hairdressers maybe with' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for alone that I've seen before include "On one's own" , "Exclusively, by oneself" , "Without others present" , "Singly" , "Isolated; exclusively" .)