Elk has right to be sulky (6)
I believe the answer is:
morose
'sulky' is the definition.
(I've seen this in another clue)
'elk has right' is the wordplay.
'elk' becomes 'moose' (synonyms).
'has' indicates putting letters inside.
'right' becomes 'r' (common abbreviation).
'moose' enclosing 'r' is 'MOROSE'.
'to be' acts as a link.
(Other definitions for morose that I've seen before include "Silent, gloomy and ill-tempered" , "dark" , "Melancholy" , "Sullen or glum." , "Gloomy and unsociable" .)