Rebecca Masterton, Dr Rebecca Masterton graduated with a BA in Japanese Language and Literature; an MA in Comparative East Asian and African Literature and a PhD in Islamic literature of West Africa. She has been... Answer updated 1 month ago

The speech of Imam al-Ridha (as) in Usul al-Kafi Vol. 1 helps to outline how Imama is established by the Qur'an.

This is a link to it, plus some other extracts from other volumes:

https://onlineshiastudies.com/imamateinquran/

The appointment of a successor was entirely in keeping with 'Allah's Sunna':

There are several verses in the Holy Qur’an that mention the Sunnah, or the Way of Allah, as follows:‘That was the Sunnah of Allah in the case of those who lived before and there will never be any change in the Sunnah of Allah.’ (Surah al-Ahzab, 33:62); ‘{Such was Our) Sunnah in the case of those whom We sent before you {to mankind), and you will never find change in Our Sunnah.’ (Surah BaniIsrail, 17:77); ‘Had the disbelievers fought against you, they would take to flight and would have found no guardian or helper. This is the Sunnah of Allah which existed before you, and you will never find any change in Allah's system’ (Surah al-Fath, 48:23); ‘[Due to] arrogance in the land and plotting of evil; but the evil plot does not encompass except its own people. Then do they await except the way of the former peoples? But you will never find in the Sunnah of Allah any change, and you will never find in the way of Allah any alteration.’ (35:43); ‘Their faith could not avail against Our punishment. Such is Allah's prevailing Sunnah (law) among His servants in the past. Thus the disbelievers are ruined.’ (Surah Mumin, 40:85).

As Dr Ibrahim Ayati explains in regard to these verses, ‘Whenever the word Sunnah has been used in the Holy Qur'an it has been used in this very literal meaning i.e. the manner in which Allah has treated the past nations. And whenever Allah says that His Sunnah is unalterable it means that there is a path for attaining to dignity and honor and He does not change it, and there is also a path and ground which leads to adversity and helplessness and that, too, is unalterable.’

The path for attaining dignity and honour is that revealed by the prophets and supported and explained by the Imams of the prophets.  This Sunnah, the sending of prophets accompanied by their supporters and successors, can be seen going all the way back to Adam [whose supporter and successor would have been Habil/Abel]. If we take a look at the prophetic lineage, we can see this.
Scholars provide an approximate outline of this lineage: ‘Adam [and his wasiy] Seth/Abel/Hibat Allah; then Noah and [his wasiy] Shem; Solomon and [his wasiy] Asaf ibn Barakhiya; Ibrahim and his succeeding awsiya Isma’il and Ishaq; Moses and his awsiya Harun and Joshua; Isa and his awsiya Simon; John and the apostles; Prophet Muhammad and his awsiya Imam 'Ali (as) and the other eleven Imams.’ (Amir-Moezzi, Shi‘ i Spirituality, p. 289).

At no time in prophetic history has a prophet not clearly stipulated his successor, and the appointment of a successor is an unchanging part of the prophetic sunnah and the Sunnah of Allah (swt).

Seth means "placed; appointed". In Judaism, Christianity and Islam, he was the third son of Adam and Eve and brother of Cain and Abel. According to Genesis 4:25, Seth was born after Abel's murder, and Eve believed God had appointed him as a replacement for Abel.]