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heir; inheritor
successor
彼は家業の跡継ぎとして育てられた。
He was raised as the heir to the family business.
跡継ぎがいなくて店を閉めることにした。
They decided to close the shop because there was no heir.
長男が跡継ぎになるのが伝統だった。
It was tradition for the eldest son to become the heir.