on the heels of
• following closely after.
• "hard on the heels of the crisis came a wave of strikes"
hot on the heels of
• following closely.
• "the gardener burst in with Mrs Cartwright hot on his heels"
Similar:
close behind,
soon after,
shortly after,
directly after,
right after,
straight after,
immediately after,
hard on the heels of,
following closely,
Opposite:
far behind,