Star heads off to find parasol (8)
I believe the answer is:
sunshade
'parasol' is the definition.
(I know that parasol can be written as sunshade)
'star heads off' is the wordplay.
'star' becomes 'sun' (the Sun is a star).
'off' indicates an anagram.
'heads' with letters rearranged gives 'shade'.
'sun'+'shade'='SUNSHADE'
'to find' is the link.
(Other definitions for sunshade that I've seen before include "protective cover" , "Awning or parasol will provide it" , "Awning or parasol, for example" , "shelter" .)