at/on somebody's heels
on (one's) heels
1. (Following) very close behind one, often persistently and to one's annoyance. I'm a preschool teacher, so I've had toddlers on my heels all day. The interior designer can't get any work done with your puppy on her heels!
2. Close to overtaking a fellow competitor. The leading candidate should be concerned about the underdog on his heels. If she does poorly on this exam, she may lose the title of valedictorian to one of the students on her heels.