Cut is harsh, one admitted, having nothing (6)
I believe the answer is:
hairdo
'cut' is the definition.
(thesaurus)
'harsh one admitted having nothing' is the wordplay.
'harsh' becomes 'hard' ('hard' can be similar in meaning to 'harsh').
'one' becomes 'i' (Roman numeral).
'admitted' is an insertion indicator.
'having nothing' becomes 'o' (I've seen this in other clues).
'hard' placed around 'i' is 'haird'.
'haird'+'o'='HAIRDO'
'is' is the link.
(Other definitions for hairdo that I've seen before include "Possibly cut" , "The process of styling head growth" , "Pageboy maybe" , "The process of styling hirsute head" , "Eg, beehive or mullet" .)