One under a mare's care

FOAL

This young horse hasn’t yet learned to gallop on its own and is often seen staying close to its mother in the field.

A mare is an adult female horse, and the word "under" hints at something in her care—like her offspring. The answer "foal" fits because it’s the term for a young horse, whether male or female, that hasn’t been weaned yet. The clue plays on the literal meaning of "under a mare’s care" to point to her baby.