Elk has right to be gloomy (6)
I believe the answer is:
morose
'gloomy' is the definition.
(morose means gloomy or sad)
'elk has right' is the wordplay.
'elk' becomes 'moose' (synonyms).
'has' is an insertion indicator.
'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, crabby" , "Miserable" , "Sullen and moody" , "blue" , "Silent, gloomy and ill-tempered" .)