Crossword Genius

Devil stalking chief primate (5)

Ross

I believe the answer is:

chimp

I'm a little stuck... Click here to teach me more about this clue!

This clue could be a double definition.

'devil stalking chief' is the first definition.
Although both the answer and definition are singular nouns, I can't understand how they can define each other.

'primate' is the second definition.
(chimp is a kind of primate)

Can you help me to learn more?

(Other definitions for chimp that I've seen before include "Anthropoid ape" , "Arboreal ape from equatorial Africa (abbr)" , "Creature" , "Cheeky primate" , "A great ape (abbr.)" .)

I've seen this clue in The Independent.
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