The leader in Cerulean City is Misty, the water-type master. You find her outside Bill's Summer Cottage on the ledge.
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In the Cerulean Gym
Misty was a gym leader since before the Pokemon series time period began. However, it was not revealed she was a gym leader until Episode 007: "Water Flowers of Cerulean City"
When he went to fight the Cerulean City gym leader, her 3 sisters were going to give him the badge without fighting, so she stepped up to uphold the honor of the gym.
Cerulean city
If you mean Misty in Cerulean, you have to go along route 25 north of cerulean to the end of the route and she will return to her gym.