Going through hairpieces, a usually hairy chap (4)
I believe the answer is:
esau
'hairy chap' is the definition.
(hairy son of Isaac in the Bible)
'going through hairpieces a usually' is the wordplay.
'going through' indicates the answer is hidden within the clue.
'ESAU' is hidden in the letters of 'hairpieces a usually'.
(Other definitions for esau that I've seen before include "Elder of the twin sons of Isaac and Rebecca" , "Son of Isaac and Rebecca" , "Twin brother of Jacob" , "Rebecca's son" , "man tricked by kid brother" .)