Personal cover (4)

I believe the answer is:

skin

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This clue could be a double definition.

'personal' is the first definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.

'cover' is the second definition.
(skin is a kind of cover)

Can you help me to learn more?

(Other definitions for skin that I've seen before include "Swindle" , "External surface" , "External membrane of body" , "Dermis" , "Flense" .)

I've seen this clue in the Evening Standard.

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