Courageous favourite losing heart (6)
I believe the answer is:
daring
'courageous' is the definition.
(thesaurus)
'favourite losing heart' is the wordplay.
'favourite' becomes 'darling' ('darling' can be a synonym of 'favourite').
'losing heart' suggests removing the centre.
'darling' with its middle taken out is 'DARING'.
(Other definitions for daring that I've seen before include "Adventurous or audaciously bold" , "Impudent - brave - courage" , "rash" , "Audacious, bold" , "Adventurous courage" .)