The relation between the last prophecy and Imamate

The relation between the last prophecy and Imamate
Generally in the view of Shias (on contrary Sunnis) all the aims and purposes in prophecy then were followed in Imamate (there are the same aims and purposes in prophecy and Imamate) therefore after the Prophet's death, all his tasks were transferred to the Imams.
The Holy Prophet Muhammad was definitely the last prophet and after his death there was no new religion:
Muhammad is not the father of any of your men but [he is] God's messenger and the Seal of the prophets. God is Aware of everything! (33/40)
Therefore after Islam there will be neither missionary (tabliqi) nor religious (tashriee) prophets. This belief is totally accepted by Muslims and is one of the religion's necessities. The one who denies it, in fact he denies the Islam and the Prophet.
The last prophecy (khatamiyat) means no other prophet will come and no other prophet will bring a new religion or commandment:
Today I have perfected your religion for you and completed My favour towards you and have consented to grant you Islam as a religion. (5/3)

Holy Prophet's tasks
Undoubtedly the Holy Prophet had many different tasks during the 23 years of his prophecy. Some of his tasks (receiving and communicating revelation) will not be continued but some others which need to be continued, listed as follows:
1- Explaining and interpreting the divine revelation
2- Explaining the new commandments on Muslims' individual and social tasks and commandments
3- Responding to the opponents of Islam and rejecting their objections to the truth of Islam
4- Guarding the religion and preventing from distortion or heresy
5- Judging the disagreements among Muslims and enforcing the general divine rules
6- Ruling over people in all political and social aspects

Imamate is all continuation of prophetic tasks. It is supposes to fulfill the prophetic purposes.

Imams' tasks
Shia Imams undertake all the Prophet's tasks and responsibilities except receiving revelation from God. The Imams are the true successors to the prophets. The following are the Imams' tasks:
1- Political rule and guidance of society
Each society has to have a ruler whether an oppressor or a good man. Of course Shias believe that the ruler should be immaculate and chosen by God
2- Religious authority
This is the most important Imam's task. They accurately explain and interpret the revelation
3- Spiritual and inner guardianship

References: the book "The relation between the last prophecy and Imamate"
The America English Quran (by T.B. Irving)
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Sources :

https://www.tahoor.com/en/Article/PrintView/119400