run after

US /rʌn ˈæf.tər/
UK /rʌn ˈæf.tər/
"run after" picture
1.

to chase or pursue someone or something

:
The dog loves to run after squirrels in the park.
She had to run after her child who suddenly darted into the street.
2.

to try to achieve or obtain something, often with great effort

:
Many young people run after fame and fortune.
He's always running after the latest trends.