on somebody’s heels

US /ɑn ˈsʌm.bə.diz hiːlz/
UK /ɑn ˈsʌm.bə.diz hiːlz/
"on somebody’s heels" picture
1.

following closely behind someone

:
The police were right on his heels after the robbery.
Success came quickly, with problems often on its heels.