Gristle regularly refused in French holiday accommodation (4)

I believe the answer is:

gite

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'french holiday accommodation' is the definition.
I don't know anything about this answer so I cannot judge whether this works.

'gristle regularly refused' is the wordplay.
'regularly refused' indicates alternate letters (letters removed at regular intervals).
The alternate letters of 'gristle' are 'GITE'.

'in' is the link.

Can you help me to learn more?

(Other definitions for gite that I've seen before include "French holiday home" , "French holiday house" , "Furnished holiday house in France" .)

I've seen this clue in The Everyman puzzle in The Observer.

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