Trinity is the character of the day in "The Perfect Match!." She was Misty's opponent in the third round, where she won with little difficulty. She lost in the final match of the Whirl Cup. She is a tough Water-type trainer.
Trinity's Gyarados was the first one that Trinity used in her battle against Misty. It is unknown if the Gyarados is her main pokemon, but it is very likely.
It reappeared in a flashback in Espeon, Not Included.