Consulate

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late Middle English (denoting the government of Rome by consuls): from Latin consulatus, from consul (see consul).

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From Latin consulātus, from consul +‎ -ātus(“ -ate”). In some senses, via French consulat.

etymonline

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consulate (n.)

late 14c., "government of Rome by the consuls," from Latin consulatus "office of a consul," from consul (see consul). Also used in reference to the consular government of France from 1799-1804. In reference to the office of a modern consul in international law, from 1702 (earlier in this sense was consulship, 1610s).