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Phrase(s): *on someone’s heels
Fig. following someone very closely; following very closely at someone’s heels. (*Typically: hard ~; hot ~; right ~. See also on someone’s tail.) • I ran as fast as I could, but the dog was still hard on my heels. • Here comes Sally, and John is hot on her heels.
McGrawhill's American Idioms And Phrasal Verbs