stalking

noun

stalk·​ing

: the act or crime of willfully and repeatedly following or harassing another person in circumstances that would cause a reasonable person to fear injury or death especially because of express or implied threats

broadly : a crime of engaging in a course of conduct directed at a person that serves no legitimate purpose and seriously alarms, annoys, or intimidates that person

Note: Stalking is often considered to be aggravated when the conduct involved also violates a restraining order protecting the victim.