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

1.
following closely behind someone
:
•
The police were right on his heels after the robbery.
•
Success came quickly, with problems often on its heels.
following closely behind someone