on sb's heels

(be) at / on sb's heels (close behind, as a constant follower or companion) — (следовать за кем-л.) по пятам; неотступно следовать за кем-л.

Example 1: The large car was on my heels during my drive into town.

Example 2: They were following close on our heels and nearly collided with us, so abruptly did we stop.