What is the clarification of the legal ruling for hijab and whether it is obligatory in the Shari‘ah?

It is obligatory for every Muslim woman who has reached the age of legal accountability (which is the age when a woman first begins menstruation), to wear the hijab. This ruling is established in the Quran, sunna, and by the consensus of the Muslim community. In the Quran, Allah the Almighty says:
O Prophet, tell your wives, your daughters, and women believers to make their outer garments hang low over them. [33:59]
In the chapter of Nur, Allah the Almighty says:
And tell believing women that they should lower their glances, guard their private parts, and not display their charms beyond what [it is acceptable] to reveal; they should let their headscarves fall to cover their necklines and not reveal their charms. [24:31]In the Prophetic traditions, the Prophet said: “O, Asmaa! If a woman reaches menarche nothing should be seen [of her body] except this and this,” and he pointed to her face and hands.1
This is the consensus of the Muslims from the earliest generations and their successors. It is necessarily known to all Muslims to be obligatory in religion.
This above answers the question.
Allah the Almighty knows best.
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Footnotes:
1. Abu Dawud, al-Sunan.