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You may be thinking about Protectorate war --- but Protectorate requires you to actually be the suzerain when you declare war. So you have to use a Protectorate casus belli before the enemy conquers the city-state.
Edit: Per the civilopedia, if you or an ally has lost a city to another civilization, you have researched Diplomatic Service, and your diplomatic relation to that other civilization is at denounced and it has been at least 5 turns, then you may declare a war of Liberation against that civ.(It is a war of Reconquest that requires you to have founded that city)