snap at someone's heels idiom
追着咬（某人）
If an animal is snapping at your heels, it is running behind you and trying to bite you.
与（某人）一决高下，对（某人）紧追不舍
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。