Let on about primate outside, and ruminant (8)
I believe the answer is:
antelope
'ruminant' is the definition.
(antelope is a kind of ruminant)
'let on about primate outside' is the wordplay.
'about' is an anagram indicator.
'primate' becomes 'ape' (large primate).
'outside' is an insertion indicator (some letters go outside others).
'let'+'on'='leton'
'leton' with letters rearranged gives 'ntelo'.
'ntelo' placed inside 'ape' is 'ANTELOPE'.
'and' acts as a link.
(Other definitions for antelope that I've seen before include "A swift-running animal like gazelle" , "Springboks, say" , "eg Eland" , "One petal for this animal" , "Hartebeest, perhaps" .)