Author due to lose heart over enemy (5)
I believe the answer is:
defoe
'author' is the definition.
(Daniel Defoe)
'due to lose heart over enemy' is the wordplay.
'to lose heart' means to remove the middle letters (I've seen 'losing heart' mean this).
'over' is a charade indicator (letters next to each other).
'enemy' becomes 'foe' (I've seen this before).
'due' with its middle taken out is 'de'.
'de'+'foe'='DEFOE'
(Other definitions for defoe that I've seen before include "See 14" , "pamphleteer and novelist" , "18th-century author" , "Daniel ---, wrote Moll Flanders" , "Daniel -, Moll Flanders author" .)