Vegetable left by a primate (5)
I believe the answer is:
potto
'primate' is the definition.
(potto is a kind of primate)
'vegetable left by a' is the wordplay.
'vegetable' becomes 'potato' (potatoes are sometimes considered vegetables).
'left by' suggests deleting specific letters (word is left or abandoned by specified letters ).
'potato' with 'a' taken away is 'POTTO'.
(Other definitions for potto that I've seen before include "Sort of 13 [LEMUR]" , "Kinkajou" , "Slow-moving African" , "Nocturnal primate" , "Little creature" .)