snap at sb's heels

If an animal is snapping at your heels, it is running behind you and trying to bite you. to compete strongly with someone and have a chance of soon defeating or replacing them: With so many younger women snapping at her heels, this year may be her last chance to win the championship

follow closely behind

چیزی که کم مونده به آدم برسه و آدم رو نفله کنه، از پا دربیاره یا شکست بده. حیوان درنده، یا ترس، یا رقیب یا غیره.