Runner perhaps started to lose heart (4)
I believe the answer is:
bean
'runner perhaps' is the definition.
'started to lose heart' is the wordplay.
'started' becomes 'began' ('begin' can be a synonym of 'start').
'to lose heart' means to remove the middle letters (I've seen 'lost heart' mean this).
'began' with its middle removed is 'BEAN'.
(Other definitions for bean that I've seen before include "Vegetable; coffee seed" , "Broad, French or kidney?" , "coffee, perhaps" , "Edible legume" , "Nut" .)