interregnum

reg stands for king or kingly styles (e.g. in regicide,regalia etc.) so inter regnum = in between two kings(referring to their ruling period).

Inter(Interval)+Regnum (Kingship)-->Interval between kingship, government etc.

inter + regime

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he interval between two reigns; any period when a state is left without a ruler

period of no (inter)fering (reg)ime