Definition of “snap at sb's heels” - English Dictionary

british dictionary

“snap at sb's heels” in British English

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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.

(Definition of “snap at sb's heels” from the Cambridge Advanced Learner's Dictionary & Thesaurus © Cambridge University Press)