Taking first of month off is cunning (4)

I believe the answer is:

arch

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'is cunning' is the definition.
(arch can mean cunning or tricksy)

I don't understand the rest of the clue.

(Other definitions for arch that I've seen before include "Roguish - superior" , "Marble, for example" , "Roguish, teasing" , "Inner side of foot" , "Instep of foot" .)

I've seen this clue in The Guardian.

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