Give chase
Definition 1 of 1
Pro Tip 1/3Action Intensity
Indicates urgent, energetic effort to catch someone or something. 
The players give chase to the ball with determination.
Pro Tip 2/3Catch Intent
Implies a strong intent to catch or apprehend rather than just following. 
The security guard gave chase to the shoplifter.
Pro Tip 3/3Immediately
Used when the pursuit is started quickly, almost instantly after the target. 
As soon as the cat ran, the dog gave chase.