tread on (one's) heels
To walk directly behind one; to follow one very closely. I'm so sick of this personal assistant treading on my heels all around the office. He knew the police were treading on his heels, but he didn't speed up or change course so that he wouldn't arouse suspicion.
ˌtread on somebody’s ˈheels
follow somebody closely: In the end she left the meeting room, with her assistant treading hard on her heels.