Cover for stars getting hot and jaded inside (8)

I believe the answer is:

sunshade

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'cover' is the definition.
(I've seen this before)

'stars getting hot and jaded inside' is the wordplay.
'stars getting' becomes 'suns' (I am not sure about this - if you are sure you should believe this answer much more).
'hot' becomes 'h'.
'and' says to put letters next to each other.
'inside' means to look at the middle letters.
The central letters of 'jaded' are 'ade'.
'suns'+'h'+'ade'='SUNSHADE'

'for' is the link.

Can you help me to learn more?

(Other definitions for sunshade that I've seen before include "shelter" , "protective cover" , "Awning or parasol, for example" , "Awning or parasol will provide it" .)

I've seen this clue in The Telegraph.

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