Keter

Kate and Peter probably met sometime in the early 2000s, when she first met Peter's nephew Derek Hale, whom Kate seduced to learn the secrets of the Hale family. Kate eventually used these secrets to stage the fire at the Hale House that killed most of Peter's family and caused him severe third-degree burns on the majority of his body that left him in a coma for six years while he slowly healed.
However, Peter was conscious throughout his coma, which gave him more than half a decade to practice and plan revenge on the Argents for the decimation of his family. When he finally woke up and regained his strength, he killed his niece Laura Hale, who had inherited his sister Talia's alpha spark after her death, so that he would have the power to create and lead his pack. Then he set out to take revenge on everyone involved in the fire, first taking out Kate's co-conspirators one by one, before pursuing Kate himself, taking advantage of the fact that he was still in a coma to disguise his identity.
Their fight reached its climax in "Code Breaker" of the first season, when Peter finally confronted Kate and forced her to apologize to Kate's niece Allison Argent, who had just learned about the supernatural world, for what she had done to the Hale family. He did not accept her apology – instead, he cut Kate's throat with his claws in the ruins of Hale House, seemingly killing her. Only a year later it turned out that Kate had survived the attack and that Peter, who was an alpha at the time, had turned her into a werejaguar. Peter found out about this just before the robbery of the Hale Vault by the benefactor's cohort and decided to ally with Kate, hoping to unite against a common enemy – Scott McCall, whom Peter mistakenly believed had stolen the power he believed was rightfully his, which Kate irrationally blamed for decimating the Argent family. Their partnership surprised even Kate, who admitted that Peter was someone she never thought she would trust him with. Unfortunately for both of them, their plan to have the McCall pack kill Scott (which allowed Peter to somehow steal his alpha powers) ultimately failed. Peter was defeated in battle by Scott, drugged with a yellow wolf spell, and locked up in the Oaks House, while Kate was forced to go on the run while being pursued by her brother Chris Argent and the Calavera hunter family. As far as is known, Kate and Peter have not been in contact since the events of "Smoke and Mirrors" of the fourth season.