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heir; inheritor
successor
一人息子が家業の後継ぎとして修行を始めた。
The only son began training as the heir to the family business.
老舗の後継ぎ問題が地方の課題になっている。
The issue of successors for long-established businesses has become a local challenge.
後継ぎがいないまま店を閉じることになった。
With no heir, the shop had to be closed.