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. 今年也许是她夺冠的最后机会，因为许多更年轻的女选手都大有后来居上之势。