Republican flees bad-tempered elk (5)
I believe the answer is:
moose
'elk' is the definition.
(I know that elk can be written as moose)
'republican flees bad-tempered' is the wordplay.
'republican' becomes 'r' (abbreviation).
'flees' is a deletion indicator.
'bad-tempered' becomes 'morose' (morose means sad or in a bad mood).
'morose' with 'r' taken out is 'MOOSE'.
(Other definitions for moose that I've seen before include "North American deer" , "beasts" , "US deer with enormous antlers" , "Ungulate" , "Animal" .)