One cutting hair in a state (5)
I believe the answer is:
maine
'a state' is the definition.
(Maine is an example)
'one cutting hair' is the wordplay.
'one' becomes 'i' (Roman numeral).
'cutting' indicates putting letters inside (some letters cut their way into a word).
'hair' becomes 'mane' (I have seen 'Long hair ' mean 'mane' so perhaps 'hair' could also mean 'mane'**).
'i' put into 'mane' is 'MAINE'.
'in' acts as a link.
(Other definitions for maine that I've seen before include "state of USA" , "NE US state" , "North-east American state" , "US state, capital Augusta (5)" , "N. US Atlantic state" .)