When does Law appear in One Piece?

Trafalgar D. Law appeared in One Piece in Episode 585 during the Punk Hazard Arc. When they entered the New World, the Straw Hat Pirates received a distress call from a group of people on an island called Punk Hazard, who stated that a samurai was attacking them.

Episode Number	Episode 585
Episode Name	"Shichibukai! Trafalgar Law"
Manga Chapter	Chapter 392

Summary of the Episode

This episode starts with Chopper, Nami and the other children trying to escape the mad scientist who was running experiments on them, they come across a room and when they enter they're shocked to see that there are frozen people inside them. In another part, Sanji and Franky defeat all the hazmat suit guys.

Sanji wants to kill the samurai as he is quite annoying as he taunts Sanji for being merciless. Franky breaks up their argument and tells Sanji not to pay heed to the samurai as he is just a mere head and then they go and try to catch up with Nami and Chopper.

Meanwhile, Brownbeard and the centaurs are in a battle with Luffy, Zoro, Usopp and Robin. Zoro manages to cut the cannonballs and Luffy deflects the other ones. When a cannonball hits their boat, they manage to paddle away to safety before anyone could drown. On the other hand, we can see Brook running away from the samurai torso and he tripped and got caught in a huge snowball.

We then see Law enter the scene and he says that the distress message didn't come from this place and mariners tend to send out these signals and transmissions to catch pirates and wanted people. When Sanji, Nami, Franky, Chopper and the kids come outside they see Law, Smoker and Tashigi and the G- 5.

Upon first glance Nami and Chopper thought that Law was behind the children's imprisonment. However, he states that he won't allow the mariners to escape so he lifts their ships with Room and Tact. Smoker tells his men that they should back off as they cannot handle Law due to his extremely powerful Devil Fruit power.