Can a Muslim lady be the head of an Islamic State? If yes, under what circumstances?
Legally, every person (man or woman) who holds the mandate of the majority has the right to form the government in an Islamic state.
However, the qualities Islam positively wants to see in a head of state show that only certain men -- not every Tom, Dick and Harry -- should ideally be selected for this great responsibility. According to the Qur’ān, the person who is elected as the head of state should have a commanding and an awe-inspiring personality and should be distinguished in integrity, wisdom and intellect. These qualities have, therefore, been cited by it as the real reason for the nomination of Tālūt (Saul) for the supreme leadership of the Israelites:
Indeed, Allah has chosen him to rule over you and has gifted him abundantly with knowledge and physique. (2:247)
It is evident from this that such elements are not suitable to head an Islamic State who lack intellect, wisdom and masculine attributes; who instead of being venturesome and enterprising are passive and receptive by nature, and who instead of influencing others are more liable to be influenced.
The reason for this is that the ruler of an Islamic State is not one who only heads them, he also leads the believers in Prayers, Hajj and Jihād. Moreover, he is like a father to his nation, and a model and a guide for them. He is the voice of their conscience and a representative of their ideology -- someone in whom their sense of honour is personified. It is vital, therefore, that he be someone who instead of delicacy has the ability to take the initiative and who instead of resignation and tenderness possess resolution and tenacity.