Someone you only call late at night when you're drunk and want to hook up, but wouldn't actually date or hang out with. Derives from late night plates of terrible food at diners that are only acceptable after 3am.
"I didn't meet anyone cool at the party last night, so I called up my late plate."
"Kristen, that guy never texts you except after midnight, when he's drunk and wants to get laid. He's late plating you!"