hard/hot on somebody's heels
1. if you are hard on someone's heels, you are following very close behind them, especially because you are trying to catch them She ran down the steps with a group of journalists hard on her heels.
2. if you are hard on the heels of someone that you are competing with, you are very close to defeating them They know we're hard on their heels and they've got to win their next three games to retain the championship.