To be chosen (from among many candidates); to be singled out for a role or responsibility.
そのプロジェクトのリーダーには彼に白羽の矢が立った。
He was chosen as the leader for that project.
数ある候補の中から白羽の矢が立つのは大変名誉なことだ。
Being selected from many candidates is a great honor.
今回の公演で主役に白羽の矢が立ったのは新入団員だった。
The newcomer was chosen for the lead role in this performance.