A shady skeleton in the cupboard? (4,6)

I believe the answer is:

dark secret

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'a shady skeleton in the cupboard?' is the definition.
I don't know anything about this answer so I can't judge whether this works.

'shady skeleton in the cupboard?' is the wordplay.
'shady' becomes 'dark' (similar in meaning).
'skeleton in the cupboard?' becomes 'secret' (I can't justify this - if you can you should believe this answer much more).
'dark'+'secret'='DARK SECRET'

Can you help me to learn more?

(Another definition for dark secret that I've seen is " something to hide".)

I've seen this clue in the Evening Standard.

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