Used to refer to the period or situation following someone's death. Often appears in formal or written contexts.
After his death, they carried on the business in accordance with his wishes.
After our father passed away, our mother raised us by herself.
Compound of 亡き (archaic adnominal form of 亡し, meaning 'dead') and 後 (after). The form 亡き is a classical Japanese attributive form that survives in fixed expressions.