Cooking is chore, family admitted (6)

I believe the answer is:

faking

'cooking' is the definition.
('fake' can be a synonym of 'cook')

'chore family admitted' is the wordplay.
'chore' becomes 'fag' (I have seen 'Tedious chore ' mean 'fag' so perhaps 'chore' could also mean 'fag').
'family' becomes 'kin' (synonyms).
'admitted' means one lot of letters goes inside another.
'fag' placed around 'kin' is 'FAKING'.

'is' acts as a link.

(Another definition for faking that I've seen is " Counterfeiting, forging".)

I've seen this clue in The Guardian.

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