Abandon course after losing heart (6)
I believe the answer is:
desert
'abandon' is the definition.
(synonyms)
'course after losing heart' is the wordplay.
'course' becomes 'dessert' (dessert is a kind of course).
'after losing heart' says to hollow out the word (remove centre letters).
'dessert' with its middle removed is 'DESERT'.
(Other definitions for desert that I've seen before include "Run away from the forces; desolate" , "ditch" , "desolate place" , "Abandon; arid region" , "Sandy wilderness" .)