Chap taking exercise is big baboon (8)
I believe the answer is:
mandrill
'big baboon' is the definition.
(I've seen this in another clue)
'chap taking exercise' is the wordplay.
'chap' becomes 'man' (chap can mean a man).
'taking' means one lot of letters go next to another.
'exercise' becomes 'drill' (military exercise).
'man'+'drill'='MANDRILL'
'is' acts as a link.
(Other definitions for mandrill that I've seen before include "Monkey with red and blue hindquarters" , "West African baboon" , "Ape" , "Baboon with colourful face" , "African baboon with red and blue muzzle and hindquarters" .)