Fast runner's beaten hare (4)
I believe the answer is:
rhea
'fast runner's' is the definition.
(bird which runs fast)
'beaten hare' is the wordplay.
'beaten' indicates anagramming the letters (letters beaten up or destroyed).
'hare' anagrammed gives 'RHEA'.
(Other definitions for rhea that I've seen before include "Fast-running flightless bird" , "Flightless bird - Greek fertility goddess" , "South American bird resembling the ostrich" , "Flightless bird -- satellite of Saturn" , "Titaness" .)