Dwindle as favourite with little energy facing defeat (5,3)
I believe the answer is:
peter out
'dwindle' is the definition.
(thesaurus)
'favourite with little energy facing defeat' is the wordplay.
'favourite' becomes 'pet' ('pet' can be a synonym of 'favourite').
'with' says to put letters next to each other.
'little' indicates taking the first letters.
'facing' means one lot of letters go next to another.
'defeat' becomes 'rout' (routing is a kind of defeating**).
The initial letter of 'energy' is 'e'.
'pet'+'e'+'rout'='PETER OUT'
'as' acts as a link.
(Other definitions for peter out that I've seen before include "Diminish feebly" , "End gradually" , "'Run down, taper off (5,3)'" , "True poet (anag) - come to nothing" , "Dwindle away to nothing" .)