Q: Could a parliament (not elected, more similar to China) exist in a caliphate as a structured form of shura or would enforcing shura be against the sharia?

A: The original system is the khilaafat system. The parliament system cannot substitute the Islamic system of Khilaafat. The parliament system is based on the majority count of hands. The person who receives the most votes from the public is elected as the president, even if the people voting for him are not committed to deen and the person himself is also not committed to deen and worthy of being appointed as the ameer according to the sharee criteria.
Hazrat Shah Waliyullah Dehlawi (rahimahulllah) mentioned in his kitaab, Izaalatul khafaa, that there are four ways in Shariah through which a person can be appointed as the khaleefah:
The first way is that the Ahlul Hill wal Aqd (i.e. the senior ulama and pious leaders of the Muslims) unanimously accept a person as the khaleefah. The example of this is found in the way Hazrat Abu Bakr (radhiyallahu 'anhu) became the khaleefah that the senior Sahaabah accepted him as the khaleefah and thereafter all the Sahaabah also accepted him.
The second way is that before the demise of the khaleefah, he appoints someone to succeed him in the position of khilaafah after his demise. The example of this is found in Hazrat Abu Bakr (radhiyallahu 'anhu) appointing Hazrat Umar (radhiyallahu 'anhu) to be the khaleefah after him.
The third way is that before the demise of the khaleefah, he forms a shura to nominate a person from among them as the khaleefah after his demise. The example of this is found in Hazrat Umar (radhiyallahu 'anhu) forming a shura and commanding them to appoint one person among them as the khaleefah after him.
The fourth way of becoming the khaleefah is through istilaa and tasallut i.e. taking control by force. An example of this type is the khilaafah of Abdul Malik bin Marwaan. This last type, though it is not the correct way to acquire khilaafah, however when the people accept the person, then he will become the khaleefah.
And Allah Ta'ala (الله تعالى) knows best.
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