Shady relative keeping cool (8)
I believe the answer is:
sinister
'shady' is the definition.
(sinister can mean shady or menacing)
'relative keeping cool' is the wordplay.
'relative' becomes 'sister' (sister is a kind of relative).
'keeping' indicates putting letters inside.
'cool' becomes 'in' ('in' can mean fashionable or cool).
'sister' going around 'in' is 'SINISTER'.
(Other definitions for sinister that I've seen before include "Threatening; evil-looking" , "Suggesting or threatening evil or danger" , ", nun going round home" , "Menacing" , "Threatening - ominous" .)