To select or single out someone from many candidates (to appoint or choose someone).
社長は次期リーダーとして若手社員に白羽の矢を立てた。
The president chose a young employee as the next leader.
監督は主役に新人俳優を白羽の矢を立てて抜擢した。
The director singled out a new actor for the lead role and promoted him.
校長は合唱団の指揮者に白羽の矢を立てた。
The principal selected someone to be the choir conductor.