Fruit pile oddly eaten by primate (5)
I believe the answer is:
apple
'fruit' is the definition.
(apple is a kind of fruit)
'pile oddly eaten by primate' is the wordplay.
'oddly' indicates alternate letters (letters in the odd-numbered positions are used).
'eaten by' means one lot of letters goes inside another.
'primate' becomes 'ape' (ape is a kind of primate).
The alternating letters of 'pile' are 'pl'.
'pl' going inside 'ape' is 'APPLE'.
(Other definitions for apple that I've seen before include "Fruit that keeps doctor away?" , "Fruit with firm white flesh" , "One poisoned Disney's Snow White" , "Sweet or tart fruit" , "pie?" .)