Is she likely to lose heart? (4)
I believe the answer is:
lily
'is she' is the definition.
'likely to lose heart?' is the wordplay.
'to lose heart?' means to remove the middle letters (I've seen 'to lose heart' mean this).
'likely' with its middle taken out is 'LILY'.
(Other definitions for lily that I've seen before include "Flower; girl's name" , "Plant like an amaryllis" , "White" , "Trumpet-shaped flowering plant" , "Plant with showy pendulous flowers" .)