Shut up keeping warm inside cover (6)
I believe the answer is:
sheath
'cover' is the definition.
(I know that sheath is a type of cover)
'shut up keeping warm' is the wordplay.
'shut up' becomes 'sh'.
'keeping' is an insertion indicator (some letters kept inside).
'warm' becomes 'heat'.
'sh' placed around 'heat' is 'SHEATH'.
'inside' is the link.
(Other definitions for sheath that I've seen before include "coat" , "case for weapon" , "Cover for a sword" , "Case for a dagger" , "cocktail dress" .)