Asian primate rushes all over the place (6)

I believe the answer is:

rhesus

'asian primate' is the definition.
(rhesus monkey)

'rushes all over the place' is the wordplay.
'all over the place' is an anagram indicator.
'rushes' anagrammed gives 'RHESUS'.

(Other definitions for rhesus that I've seen before include "Blood type or kind of monkey (6)" , "Kind of monkey (or factor)" , "Monkey - factor in blood cell problem" , "Small Indian monkey" , "The Rh in "Rh factor"" .)

I've seen this clue in The Guardian.

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