En famille, regularly supplying cover (4)

I believe the answer is:

nail

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'cover' is the definition.
The answer and definition can be both man-made objects as well as being singular nouns.
Perhaps you can see a link between them that I can't see?

'en famille regularly' is the wordplay.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'en'+'famille'='enfamille'
The alternate letters of 'enfamille' are 'NAIL'.

'supplying' is the link.

Can you help me to learn more?

(Other definitions for nail that I've seen before include "Part of finger" , "Metal spike with head" , "Handy tip" , "Apprehend" , "SECOND PART OF 17" .)

I've seen this clue in The Times.

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