To report or inform (often a formal/written expression; alternate form of 報じる).
警察は事故の状況を直ちに本部に報ずるべきだ。
The police should report the accident situation to headquarters immediately.
記者は現場から事件の詳細を報ずる役目を果たした。
The reporter fulfilled the role of reporting the incident details from the scene.
結果が出次第、上司に報ずること。
Report to your superior as soon as the results come out.
To repay or requite (an older/literary usage meaning to give recompense or return).
彼の恩にどう報ずるべきか分からない。
I don't know how to repay his kindness.
悪事はいつか天が報ずるだろう（やや文語的表現）。
Wrongdoing will be requited by heaven someday (somewhat literary).