Drink sent back by the French primate (5)
I believe the answer is:
lemur
'primate' is the definition.
(I know that lemur is a type of primate)
'drink sent back by the french' is the wordplay.
'drink' becomes 'rum' (rum is a kind of drink).
'sent back' says the letters should be written in reverse.
'by' means one lot of letters go next to another.
'the french' becomes 'le' ('the' in French).
'rum' written backwards gives 'mur'.
'mur' after 'le' is 'LEMUR'.
(Other definitions for lemur that I've seen before include "Arboreal animal" , "Tree-living primate" , "Monkey-like animal of Madagascar" , "Large-eyed animal with foxy face and furry tail" , "Madagascan monkey" .)