run after

Short definition from Wiktionary

Verb

1. 1
   To follow quickly, often in an effort to catch or catch up with (someone or something).
2. 2
   To make a determined effort to win someone's affections or to have a sexual relationship with them.
3. 3
   To endeavour to find or obtain.
4. 4
   To seek the company or assistance of; to frequent; to consult (someone).
5. 5
   To seek to participate in, devote oneself to (something).
6. 6
   To be well-liked and much admired.