Part of the neck of northern primate (4)
I believe the answer is:
nape
'part of the neck' is the definition.
('nape' is part of 'neck')
'northern primate' is the wordplay.
'northern' becomes 'n' (abbreviation e.g. N. Ireland).
'primate' becomes 'ape' (I've seen this before).
'n'+'ape'='NAPE'
'of' acts as a link.
(Other definitions for nape that I've seen before include "sofa" , "It's a pane in the neck" , "Scruff of the neck" , "Back part of the neck" , "Scrag" .)