The Quran is the book of divine law, human cultivation, the book of wisdom and divine guidance whose agenda is to inform, educate and train in morals, beliefs and practice.
The Quran mainly addresses issues, especially ahkam, from a general perspective, leaving the specifics to the Prophet (sa) and his successors, the true interpreters (as); such as prayer, fasting, zakat, hajj etcImamate is also one of these issues which have been generally reflected.
Considering that we have thoroughly answered this question in previous articles that can be found in this very website, we will give a brief explanation and refer you to other articles.
The shan nuzul (the circumstances of revelation) of numerous verses in the Quran, such as Ayah of Tabligh (Maeda, 67), Ayah of Wilayah (Maeda, 55), Ayah of Ulul Amr (Nesa, 59), Ayah of Sadeqeen (Tobeh, 119) revolve around the issue of Imamate.
It is necessary to mention that Allameh Hilli (ra) has written a book titled Alfain, that consists of a thousand reasons in favor of the Imamate of Imam Ali (as) and a thousand answers to the objections made against his Imamate, among which a great number of these reasons are from the Quran and can be referred to if needed.
Also, the eighth section of the seventh volume of Bihar al- Anwar of Imamate has listed the ayahs revealed regarding Imamate under the title Ayahs regarding revealed about the Imams (as).
For more information please refer to following answers below that can be found on this website.
The Quran and the Imamate of Ali (as), Question 1817.
Proving Imamate in the Quran, Quesitn 4729
The Imamate of Imam Ali (as), Question 7554
Proving Imam Alis Imamate, Question 1162
 Hilli, Hasan bin Yusuf, Al-Alfain, Dar al-Hijrah, Qom, 1409 (AH).
 Allamah Majlisi, Bihar al-Anwar, (the section on imamate, Farsi translation of the seventh volume), Khosravi, Musa, publisher: Islamiyyah