A formal written request or petition submitted to an authority, such as a government office or organization.
市役所に補助金の願い出を提出した。
I submitted an application for a subsidy to the city office.
住民たちは道路拡張の願い出を出した。
The residents filed a petition for road expansion.
Compound of 願い (negai, 'wish, request') and 出 (de, from 出る, 'to go out, submit'). The combination conveys the act of submitting a request.