1
general::
Phrase(s): run after someone or something
Go to after someone or something., Phrase(s): run after someone
to chase someone of the opposite sex hoping for a date or some attention. • Is John still running after Ann? • No, Ann is running after John.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Also, chase after. 1. Follow, pursue with haste, as in Our dog loves to run after the mail truck, or The children were chasing after the geese in the park. [c. 1300] 2. Seek the company or attention of, especially aggressively. For example, He's run after her for a year, but she just ignores him. [Early 1500s]
American Heritage Idioms