Funds for project wife set aside - most shrewd (7)

I believe the answer is:

archest

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'funds for project wife' is the definition.
I can't judge whether this definition defines the answer.

'set aside most shrewd' is the wordplay.
I cannot quite see how this works, but
an anagram of 'set' is 'est' which is present in the answer.
'shrewd' could be 'arch' (I've seen this before) and 'arch' is located in the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

I've seen this clue in The Independent.

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