Indian princess has hair a man styled (8)
I believe the answer is:
maharani
'indian princess' is the definition.
(I've seen this before)
'hair a man styled' is the wordplay.
'styled' is an anagram indicator.
'hair'+'a'+'man'='hairaman'
'hairaman' anagrammed gives 'MAHARANI'.
'has' is the link.
(Other definitions for maharani that I've seen before include "Wife of a maharaja" , "Indian widow" , "Indian princess" , "Indian ruler's wife" .)