Elk has right to be sullen (6)
I believe the answer is:
morose
'sullen' is the definition.
(both mean miserable)
'elk has right' is the wordplay.
'elk' becomes 'moose' (synonyms).
'has' indicates putting letters inside.
'right' becomes 'r' (common abbreviation).
'moose' placed around 'r' is 'MOROSE'.
'to be' is the link.
(Other definitions for morose that I've seen before include "Sullen or glum." , "Sullen. bad-tempered" , "Peevish and gloomy" , "Moody, glum" , "Down in the dumps" .)