Homework covering principal rule of two (7)

I believe the answer is:

diarchy

'rule of two' is the definition.
(government by two independent authorities)

'homework covering principal' is the wordplay.
'homework' becomes 'diy' (DIY is work done on your home).
'covering' indicates putting letters inside.
'principal' becomes 'arch' (as in arch-enemy).
'diy' enclosing 'arch' is 'DIARCHY'.

I've seen this clue in The Guardian.

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