To make a name for oneself; to achieve notable success or start a venture and succeed.
若者は地元で一旗あげようと、小さな店を開いた。
The young man opened a small shop in his hometown hoping to make a name for himself.
彼女は国際大会で優勝して一旗あげた。
She made a name for herself by winning the international tournament.
そのスタートアップが新しい市場で一旗あげる可能性は高い。
That startup has a good chance of making a mark in the new market.