Does a married man need the permission of his first wife to re-marry according to the Sharia?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

As for your question about the second wife, there is nothing in the Sharee‘ah (Islamic law) that proves the unlawfulness of a man marrying a second wife without the consent of his first wife. However, a group of scholars made it lawful for a woman to make it a condition for the man who proposes to marry her that he must not get married to any other woman as long as she is his wife. For these scholars, if the man accepts this condition, he must fulfill it. Their evidence is the Hadeeth of ‘Uqbah Ibn ‘Aamer, may Allaah be pleased upon him, that the Prophet Muhammad said: “The most worthy conditions to be fulfilled by you (Muslim men) are the ones by which you made the (women’s) vagina lawful to you.” This is a sound Hadeeth narrated by Al-Bukhaari and others. But this condition is false and the man is not asked to fulfill it because it goes against the Quran which has made it lawful for the man to marry two, three or four women. Allah Says (what means): {…then marry women of your choice two or three or four.} [Quran 4:2]

Besides, the Prophet said: “Whoever stipulates a condition that is not in the Book of Allah (i.e. Quran), it is considered false even if he stipulates a hundred conditions.” [Al-Bukhari and Muslim]

For more benefit that a husband does not need the permission of his first wife to take a second wife, please refer to Fataawa 121947, 82988, and 84411.

Allah knows best.