Girl likely to lose heart (4)
I believe the answer is:
lily
'girl' is the definition.
(girl's name)
'likely to lose heart' is the wordplay.
'to lose heart' says to hollow out the word (remove centre letters) (I've seen 'lost heart' mean this).
'likely' with its middle removed is 'LILY'.
(Other definitions for lily that I've seen before include "White" , "Tiger -; water -" , "Flower, maybe of the valley" , "Plant with large trumpet-shaped flowers" , "Plant with showy pendulous flowers" .)