Run after chap for fruit (5)
I believe the answer is:
mango
'fruit' is the definition.
(mango is a kind of fruit)
'run after chap' is the wordplay.
'run' becomes 'go' ('go' can be a synonym of 'run'**).
'after' says to put letters next to each other.
'chap' becomes 'man' (I've seen this before).
'go' after 'man' is 'MANGO'.
'for' is the link.
(Other definitions for mango that I've seen before include "Once exotic fruit" , "Type of fruit" , "Asian fruit" , "Large oval tropical fruit" , "Ovoid edible fruit" .)