to follow (somebody or something) rapidly or persistently
to cause (somebody or something) to depart or flee
chiefly Brit (+ up) to investigate (a matter) or contact (a person, company, etc) in order to obtain information or hasten results
informal to attempt to establish a romantic or sexual relationship with (somebody) in a persistent or unsubtle manner
(+ after) to chase an animal, person, or thing
to rush or hasten