God, the Glorified, makes a clear reference to the issue of interregnum (cessation) in verse 19 of Chapter al-Maedah where he says:

یا أَهْلَ الْکِتابِ قَدْ جاءَکُمْ رَسُولُنا یُبَیِّنُ لَکُمْ عَلى فَتْرَة مِنَ الرُّسُلِ أَنْ تَقُولُوا ما جاءَنا مِنْ بَشیر وَ لا نَذیر»

"O followers of the Book! indeed Our Messenger has come to you explaining to you after a cessation of the (mission of the) messengers, lest you say: There came not to us a giver of good news or a warner, so indeed there has come to you a giver of good news and a warner; and Allah has power over all things."
The Holy Quran names the time gap between the prophethood of Prophet Jesus (AS) and that of the Last of Prophets (S) as the period of "cessation of prophets" (fatrat). The word "fatrat" is derived from the root word "fatr" which literally means calm and relaxation.  Raghib Isfahani says:  Fotur refers to calm prevailing after an extreme situation, ease after hardship and weakness after strength.[1]
Fatrat (cessation) according to Muslim exegetes and theologians refers to a period in which revelation has ceased and the prophet does not have a code of practice (shari”ah) to propagate.[2] In other words, the period which is a period of interval and cessation of revelation, a period characterized by calm and recess and in which there was no messenger and warner was called fatrat[3]. Of course, it should be noted that although there was no messenger during the period of cessation but there was a divine religion which people had to follow.[4]
In the time period between Moses and Jesus, there were prophets and messengers but as per the foregoing verses, it seems that there were no prophets nor was there any revelation following Prophet Jesus (AS) and the time period between him and the Prophet of Islam (S). God, the Glorified, did not send any prophets or warner with a divine miracle.[5] That is why the Quran describes this period as the period of "cession of messengers".
On the other hand, as per historical reports and narrations,[6] in order for the divine rules, instructions, injunctions and signs not to disappear, the earth has never been devoid of a hujjah (divine authority), visible or invisible, known or unknown. Through them, Allah preserves and maintains his sings and symbols so as to surrender them to people like themselves and that their seeds may be cultivated in the hearts of people like them.  That is why Muslim exegetes unanimously agree that even though there were no prophets or messengers with a shari”ah during this period, there would be no problem if there lived some of the successors or even a prophet without shari”ah within this time period. Because there were prophets who had been sent to guide the people. Some of them were from the children of Israel and some others were Arabs.[7]
Allamah Tabatabai says in this regard, "Fatrat means that a prophet with a shari”ah and book has not been sent. It does not means that God did not send any prophets during the time period between Jesus and the Prophet of Islam, peace be upon him and his family.[8]
Mas”udi (d. 346 A.H.) says in Moruj al-Zahab:  There were a group of monotheists in the time period between Jesus Christ and Muhammad (S) who believed in the day of resurrection.  There are some differences about them with some scholars saying they were not prophets. [9] The names of some of them are the following: Khalid bin Senan Isa[10], Hanzalah bin Safwan,[11] Girgis,[12] Simon[13] etc.
Also, after the ascension of Jesus, his disciples who were twelve people[14] lived after him and spread his religion in the world.
In this regard, there are traditions which, regardless of their authentication, refers to the chain of successorship from Adam (AS) to the Last of Prophets (S) until the last Hujjah, the Imam of Time (atf):
The Holy Prophet of Islam (S) has been reported to have said:

"I am the lord of Prophets, and my successor (wasi) is the lord of successors, and my successors are the lords of successors. Adam asked Allah to give him a righteous successor, Allah told him: I have honored Prophets with Prophethood, and selected My creations and I chose the best of them as successors. Then Allah, the Exalted, revealed to Adam to appoint Sheith … and he made his son his wasi. Shaban made Mahleth his wasi, he then appointed Mahooq his successor who in turned appointed Umaisha as his successor. Then he appointed Akhnukh who appointed Prophet Idris as wasi.  Idris appointed Nahoor as his wasi,... Nooh’s Wasi was Saam. Saam passed the successorship to Uthamer, Uthamer to Bar”ayshasha and he to Yafeth, he to Barah, he to Jufaysah, he to Imran and he to Ibrahim to his son Ismael, and Ismael to Ishaaq, and Ishaaq to Ya’qub, and Ya’qub to Yusuf ... and Moosa son of ‘Imran to Yusha’ son of Non, and Yusha’ to Dawood, and Daawood to Solayman, and Solayman to Aasef Barkhiya ... and ‘Isa to Sham’un Safa, he to Yahya Zackhariya and he to Munzir and he to Salima and Salima to Barda. The Messenger of Allah  said, Barda passed the successorship to me and I (Mohammad (S)) give my wesaayat to you ‘Ali, and you to your successor, and he to your successors from your offspring one after the other, so that it (wesayat or successorship) will reach the best of the people of the earth, after you."[15]
Imam Ali (AS) says: "The earth is never devoid of those who maintain Allah”s plea either openly and reputedly or, being afraid, as hidden in order that Allah”s pleas and proofs should not be rebutted. How many are they and where are they? By Allah, they are few in number, but they are great in esteem before Allah. Through them Allah guards His pleas and proofs till they entrust them to others like themselves and sow the seeds thereof in the hearts of those who are similar to them."[16]
Kumayl, one of the companions of the Commander of the Faithful, Ali (AS) says:   I was in Hazrat Ali”s company. He sighed and said, "The earth will never be empty of one who establishes the proof of Allah, whether overtly with publicity or fearfully in obscurity, lest Allah”s proofs and elucidations come to naught."[17]
In another lengthy tradition, it has been reported: "After the demise of Ismail (son of Imam Sadiq), a number of the Imam”s companions who thought Ismail was the next Imam after him, began to doubt thinking they were going to remain without an imam. Thus, they approached Imam Sadiq (AS) who answered to them as such:

«هیهات هیهات أبى الله و الله أن ینقطع هذا الأمر حتى ینقطع اللیل و النهار»

It is not as such and imamate will not cease until the day and night come to an end.[18]
Sheikh Saduq (AS) narrates a tradition in Kamal al-Deen which signifies that the earth is not and will not be empty of a divine authority from creation of Adam until the day of Judgement.[19] Therefore, it is necessary that there should be a divine authority at all times so that the world is maintained, irrespective of whether people know that authority or he remains unknown in the earth.
The conclusion drawn out is that:
1. The phrase "cessation of prophets" signifies that there is no messenger with a shari”ah but it does not negate the existence of a wasi (successor) or a prophet without shari”ah. Therefore, during the period of cessation, there were successors or prophets who openly engaged in preaching or were hidden among people so that the earth would not be without a divine authority. Thus, the earth has never been empty of a divine authority during the period of cessation.
2. The existence of a divine authority in the period of cessation between Prophet Jesus (AS) and the Prophet of Islam (S) can be assumed in the following ways:
A) According to Muslims, Prophet Jesus (AS) is alive and he was never crucified. Therefore, Jesus has never been absent until the advent of the Prophet of Islam. He is still living in the earth.
B) He also had successors some of whom were known and some unknown.

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