Is it obligatory for women to cover their heads during Azan or when reciting the Qur'an?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

If the questioner means is it compulsory to cover the head if a woman who calls Azan for women only or at the time of reciting the Qur'an? The answer is that it is not compulsory but doing so is likeable.
If she is asking about covering head when they hear Azan or recitation of the Qur'an, then the answer is that doing so is not demanded. So, it is neither compulsory nor likeable.
Allah knows best.