Primate, person taking exercise (8)
I believe the answer is:
mandrill
'primate' is the definition.
(I know that Mandrill is a type of Papio)
'person taking exercise' is the wordplay.
'person' becomes 'man' (man is a kind of person).
'taking' is a charade indicator (letters next to each other).
'exercise' becomes 'drill' (synonyms).
'man'+'drill'='MANDRILL'
(Other definitions for mandrill that I've seen before include "Large baboon" , "Monkey with red and blue hindquarters" , "West African baboon-like primate" , "Ape" , "Baboon with colourful face" .)