Primate has quietly left fruit (5)
I believe the answer is:
apple
'fruit' is the definition.
(I know that apple is a type of fruit)
'primate has quietly left' is the wordplay.
'primate' becomes 'ape' (large primate).
'has' indicates putting letters inside.
'quietly' becomes 'p' (p for piano and quiet).
'left' becomes 'l' (common abbreviation).
'p'+'l'='pl'
'ape' placed around 'pl' is 'APPLE'.
(Other definitions for apple that I've seen before include "Firm round fruit" , "Crisp fruit" , "German fruity dessert" , "One poisoned Disney's Snow White" , "Fruit that keeps doctor away?" .)