Bandana person used to cover part of neck (4)
I believe the answer is:
nape
'part of neck' is the definition.
('nape' is part of 'neck')
'bandana person used to cover' is the wordplay.
'to cover' indicates a hidden word (I've seen 'covering' mean this).
'NAPE' is hidden in the letters of 'bandana person used'.
(Other definitions for nape that I've seen before include "Back part of the neck" , "Scruff of the neck" , "It's a pane in the neck" , "Scrag" , "sofa" .)