at somebody's heels
1. if you are at someone's heels, you are following very close behind them Dr Grange walked through the ward with a group of student doctors at his heels.
2. if you are at the heels of someone that you are competing with, you are very close to defeating them With so many promising young contenders at his heels, Roper can't afford to make any mistakes. There are many younger women snapping at her heels, eager to replace her as company director.