take after someone—
1. resemble a parent or ancestor in character or appearance:
- I take after my mother in looks, but people say I’ve got my father’s character.
2. set out in pursuit of a person:
- Victoria, enraged, ends up in the path of a bucket of water and takes after the brutish men with a broom.
take off after someone—(also: take out after someone) = take after someone 2:
- Claire took off after the robbers, screaming, “Stop thief !” as loudly as she could.