1Later; afterwards — a somewhat formal, literary word for the time following an event, usually written in kana. A classic example is 「雨のち晴れ」 (rain, later clear) in weather forecasts. Everyday speech uses あと instead.
明日の天気は雨のち晴れの予報です。
Tomorrow's forecast is rain, later turning clear.
その知らせを聞いたのち、彼は静かに席を立った。
After hearing the news, he quietly rose from his seat.
契約はよく確認したのちに署名してください。
Please sign the contract only after checking it carefully.
2The future; a later time. Often used as 「のちに」 with a more formal tone than あとで.
のちに彼はこの町の市長となった。
He later became the mayor of this town.
この決断が、のちの人生を大きく変えた。
This decision greatly changed his later life.
3(Literary) after a person's death; used in the phrase 亡きのち to refer to the time after someone has passed away — an old-fashioned expression.
祖父の亡きのち、家はすっかり寂しくなった。
After my grandfather passed away, the house grew utterly lonely.
4(Archaic) a descendant; offspring. An old usage rarely seen in modern Japanese.
その一族ののちには、多くの名士が現れた。
Among that clan's descendants, many distinguished figures appeared.