Thou wilt not cut off my seed after me; as princes use to destroy their competitors, and those that have any hopes of or pretence to their crown; and Saul had endeavoured to destroy David for the same reason, and therefore he feared a retaliation. Thou wilt not destroy my name, to wit, by cutting off my seed. So it is the same thing repeated in other words, as is usual in Scripture.
Related Commentaries of 1 Samuel 24:21
1 Samuel 24:21
21 Swear now therefore unto me by the LORD, that thou wilt not cut off my seed after me, and that thou wilt not destroy my name out of my father's house.