動き出す

start moving, begin to move, take action, make a move

動き move + 出す pay (money or expenses)
verb Rare #45,647
start moving, begin to move
JA: 電車がゆっくり動き出す。
EN: The train starts moving slowly.
take action, make a move
JA: 彼は明日から動き出す。
EN: He'll start taking action tomorrow.

今日中にホシはきっと動き出す

Hoshi is sure to make a move today.

— High and Low (1963)

ジョージは、列車が動き出すのを感じた。

George felt the train start moving.

まもなく彼は病気が治って動き出すだろう。

He’ll recover from his illness and be up and about soon.