The 19-year-old singer joined Stewart, his wife Penny Lancaster and their 33-year-old daughter for a meal in Los Angeles, reported Contactmusic.
Styles was seen kissing and holding hands with Kimberley.
"They weren't exactly hiding it. Rod was well aware what was going on and didn't seem to mind. Harry's well-known for his thing for older women, and Kimberley is a striking blonde so it's easy to see the appeal," said a source.
His bandmate Louis Tomlinson recently claimed that he helps the Styles to flirt with girls.
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