Activity handymen do, maintaining cunning system with two rulers (7)

I believe the answer is:

diarchy

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'with two rulers' is the definition.
Although both the answer and definition are singular nouns, I can't understand how one could define the other.

'activity handymen do maintaining cunning system' is the wordplay.
I cannot really understand how this works, but
'cunning' could be 'arch' (arch can mean cunning or tricksy) and 'arch' is present in the answer.
The remaining letters 'diy' is a valid word which might be clued in a way I don't see.
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 Times.

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