to (one's) hand: (esp. of an animal) under (one's) control, into subjection. Frequently in to bring to hand.

In (or into) subjection; under rule or command. Obsolete.

under subordination: under the authority or control of another. Also with of, to. Also in under the subordination of.

Originally of a horse (later of a person, emotion, etc.): under firm control, subject to discipline (chiefly in to keep in hand). Now also more…