Monarch's rule is unfamiliar except for Republican's predecessors (5)

I believe the answer is:

reign

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'monarch's rule' is the definition.
(I've seen this in another clue)

I can't explain the remainder of the clue.

(Other definitions for reign that I've seen before include "Govern" , "Period of monarch" , "Rule over in Niger" , "Predominance" , "Spell in office" .)

I've seen this clue in The Times.

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