Matt Rife, who dated the British actress for almost a year in 2017, has nothing but the best wishes for the new couple, but warns Pete to "be careful."
In a candid new chat with TMZ outside The "Laugh Factory" in Los Angeles, where he first met Kate, Matt says, "We dated for a year and it was complicated - a lot of ups and downs. She moved on and I'm happy..."
Asked if he has any tips for the new man in Kate's life, Matt thought long and hard and then offered up, "Run! Enjoy it while you can... Just be careful."
He then added, "I hope they're both happy. I hope that it can build to where it's an established, good relationship..."
Revealing he hasn't spoken to his ex - or Pete - "for a while," Rife also made it clear he's not interested in winning Kate back.
"Not a chance," he said when asked if he would be interested in reconciling with his ex.
Pete and Kate have been getting close over the last couple months, and even his ex-fiancee Ariana Grande believe they make a good couple.
The pair confirmed the romance by kissing passionately as they watched an ice hockey game together on Sunday, March 03 at Madison Square Garden in New York.
The pair was photographed holding hands, heading into the venue, and Kate kissed and cuddled her new man, who is just five years older than the actress' daughter Lily, as they sat in the stands watching the game.
Their day out came after Kate also joined Pete at the after-party following the most recent episode of "Saturday Night Live", on which he is a regular.