hot on somebody's heels

Từ điển Oxford Advanced Learner 8th

▪ I. (hard/hot) on sb's/sth's ˈheels idiom
very close behind sb/sth; very soon after sth
•News of rising unemployment followed hard on the heels of falling export figures.
•He ran ahead, with the others hot on his heels
Main entry: ↑heel_idiom
 
▪ II. hot on sb's/sth's ˈheels idiom
following sb/sth very closely
•He turned and fled with Peter hot on his heels.
•Further successes came hot on the heels of her first best-selling novel.
Main entry: ↑hot_idiom