継 (Kanji for succeed / inherit)

not 'succeed' like to win, but to succeed someone at a position.

Onyomi

KEI

It's OK to inherit a ball of string and a bag of rice from a loser.

つ*ぐ	to inherit. Or to get a job because the last person quit. Or to become king, because the old king got mysteriously sick and died. ★★★☆☆

跡継ぎ(あとつぎ)

heir/heiress ☆☆☆☆☆
跡 (vestiges) + 継 (succeed / inherit) = 跡継ぎ (heir/heiress)

an inheritor, an heir, heiress

継続(けいぞく) する

to carry on ☆☆☆☆☆
継 (succeed / inherit) + 続 (continue) = 継続 (to carry on)

to carry on (the family business / a tradition)