chase_after
1. [ verb ] pursue someone sexually or romantically
Synonyms: chase
Related terms: woo pursuit
2. [ verb ] go after with the intent to catch
Synonyms: chase go_after trail dog track give_chase tag tail
Examples:

"The policeman chased the mugger down the alley" "the dog chased the rabbit"

Related terms: pursue hound quest run_down chase_away tag_along pursuit pursuer lead tag tail trailing chaser