In James, a uniquely hairy man (4)
I believe the answer is:
esau
'hairy man' is the definition.
(hairy son of Isaac in the Bible)
'in james a uniquely' is the wordplay.
'in' indicates a hidden word.
'ESAU' is hidden within 'james a uniquely'.
(Other definitions for esau that I've seen before include "Biblical twin to Jacob" , "Isaac's eldest son" , "scriptural character" , "Old Testament twin" , "Hairy OT man" .)