Elk has right to be glum (6)
I believe the answer is:
morose
'be glum' is the definition.
(synonyms)
'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' acts as a link.
(Other definitions for morose that I've seen before include "blue" , "Surly and unforthcoming" , "Miserable" , "Sullen and brooding" , "Lugubrious" .)