date up

verb2

1. •
   (informal) To date someone who is more desirable or of a higher social status than oneself.

   • The growing number of women now ‘dating up’ with sugar daddies has led to a strange new creature emerging from the depths. He’s suave, charming and wants to date you. Oh and he’s totally... skint. — 2021
2. •
   (slang, old-fashioned) To have an affair or dalliance with (someone).