‘Ali ‘Abd al-Raziq, a graduate of Al-Azhar who was subsequently stripped of his qualifications, wrote in Al-Islam wa usul al-hukm (Islam and the fundamentals of ruling):

“We do not find any of the previous scholars who made the claim that the establishment of the Imam is an obligation, trying to establish evidence for that claim using any verses from the Book of Allah” [Al-Islam wa usul al-hukm, 1925]

In sharp contrast to this, the Syrian historian and former Carnegie scholar Sami Moubayed wrote in the Daily Telegraph:
“All pious Muslims well-read in the Hadith (the compiled sayings of the Prophet*) firmly believe in the need to establish an Islamic State headed by a Muslim Caliph. This is mentioned twice in the Holy Quran and it’s central to the Islamic faith. No Muslim scholar would debate an Islamic state and the caliphate.” [Daily Telegraph, 23rd September, 2015][*ﷺ]

Significantly, Dr. Moubayed makes reference to the Sunnah of the Prophet ﷺ as well as the Qur’an. The hadiths relating to the obligation of the Caliphate cannot be ignored by any Orthodox Muslim, as Sunnis are required to refer to both the Qur’an and the Sunnah as the main sources of the dīn (see here for a discussion of this point). Some of these hadiths are mentioned here.

Dr. Moubayed also states that in fact the Caliphate imperative is mentioned in the Quran, so let us examine the āyahs which refer to this topic.

The most commonly cited verse in this regard is in Surah al-Baqarah:

When your Lord said to the angels, ‘I am putting a caliph [khalīfah] on the earth,’ they said, ‘Why put on it one who will cause great corruption on it and shed blood when we glorify You with praise and proclaim Your purity? He said, ‘I know what you do not know.’

In his famous exegesis (tafsīr) of the Qur’an, Ibn Kathir comments:

“Al-Qurtubi, as well as other scholars, said that this Āyah (2:30) proves the obligation of appointing a Khalīfah to pass judgements on matters of dispute between people, to aid the oppressed against the oppressor, to implement the Islamic penal code and to forbid evil. There are many tasks that can only be fulfilled by appointing the Imam, and what is necessary in performing an obligation, is an obligation itself.” [Tafsir Ibn Kathir, Vol. 1 p. 185]

And here is what Al-Qurtubi states in his tafsīr:

“This āyah is sound evidence for having a leader and a caliph who is obeyed so that he will be a focus for the cohesion of society and the rulings of the caliphate will [be] carried out. None of the Imams of the Community disagree about the obligatory nature of having such a leader, except for what is related from al-Aṣamm (lit. the Deaf), who lived up to the meaning of his name and was indeed deaf to the Sharī‘ah, and those who take his position who say that the caliphate is merely permitted rather than mandatory if the Community undertakes all their obligations on their own without the need for a ruler to enforce them. Our evidence is found in the words of Allah Almighty: ‘I am putting a caliph on the earth’ as well as other āyahs (38:26, 24:55)”
[Abu ‘Abdullah Muhammad ibn Ahmad al-Qurtubi, Tafsīr al-Qurṭubī: The General Judgments of the Qur’an and Clarification of what it contains of the Sunnah and Āyahs of Discrimination, Vol. 1, translated by Aisha Bewley, Diwan Press, 2019, pp. 148-149]

So there are more verses in the Qur’an which mention the caliphate:

O Dawud! Verily, We have placed you as a successor [khalīfah] on the earth; so judge you between men in truth (and justice) and follow not your desire — for it will mislead you from the path of Allah. Verily, those who wander astray from the path of Allah (shall) have a severe torment, because they forgot the Day of Reckoning. [38:26]

In his tafsīr, Ibn Kathir states:

“This is advice from Allah, may He be exalted, to those who are in positions of authority. They should rule according to the truth and justice revealed from Him, they should not turn away from it and be led astray from the path of Allah. Allah has issued a stern warning of a severe punishment to those who go astray from His path and forget the Day of Resurrection.

Ibn Abi Hatim recorded that Ibrahim Abu Zur‘ah, who read the Scripture, reported that Al-Walid bin ‘Abd al-Malik said to him: ‘Does anyone have the right to question the Khalīfah? You have read the first Scripture and the Qur’an, and you have understood them.’ He replied, ‘May I speak, O Commander of the faithful?’ He said, ‘Speak, for you are under the protection of Allah.’ I said, ‘O Commander of the faithful, are you more dear to Allah, or Dawud, peace be upon him? For Allah gave him both prophethood and rulership, then He warned him in His Book:
O Dawud ! Verily, We have placed you as a successor [khalīfah] on the earth; so judge you between men in truth (and justice) and follow not your desire – for it will mislead you from the path of Allah [38:26]” [Tafsir Ibn Kathir, vol. 8, p. 324]

Finally,  there is a verse in Surah al-Nur:

Allah has promised those among you who believe and do righteous good deeds, that He will certainly grant them succession [khilāfah] in the land, as He granted it to those before them, and that He will grant them the authority to practise their religion which He has chosen for them. And He will surely give them in exchange a safe security after their fear if they worship Me and do not associate anything with Me. But whoever disbelieved after this, they are the rebellious [24:55].

Ibn Kathir comments in his tafsīr:
“This is a promise from Allah – the Most High – to His Messenger ﷺ that He would cause his Ummah to become successors [khulafā’] on earth, i.e., they would become the leaders and rulers of mankind, through whom He would reform the world and to whom people would submit, so that they would have in exchange a safe security after their fear. This is what Allah did indeed do, may He be glorified and exalted, and to Him be praise and blessings. For He did not cause His Messenger ﷺ to die until He had given him victory over Makkah, Khaybar, Bahrain, all of the Arabian Peninsula and Yemen; and he took Jizyah from the Zoroastrians of Hajar and from some of the border lands of Syria; and he exchanged gifts with Heraclius the ruler of Byzantium, the ruler of Egypt and Alexandria, the Muqawqis, the kings of Oman and An-Najashi of Abyssinia, who had become king after Ashamah, may Allah have mercy on him and grant him honour.”
[Tafsir Ibn Kathir, vol. 7, pp. 113-114]