on the move
Busily moving about, very active, as in A nurse is on the move all day long. [Mid-1800s] Also see on the go.
Going from one place to another, traveling, as in Our troops are on the move again, or Ruth and Dick are always on the move, never staying put for more than a month or two. [Late 1700s]
Making progress, advancing, as in Their technology is clearly on the move.