Nikah halala

In Sharia law a couple who divorce cannot remarry each other for a third time unless the woman is already married.

According to All India Muslim Personal Law Board a man cannot remarry a woman after triple talaq unless she has already consummated her marriage with another man and then that new husband dies or divorces her. In this case the marriage (Nikah) of the woman with her new husband is called Nikah halala.

According to the Sharia if a husband divorces his wife by pronouncing talaq, he can revoke the divorce within the iddah, that is, the period of separation that precedes divorce. If the divorce is completed, the couple can remarry. The couple may divorce and remarry twice. However, if they divorce a third time, they can neither unite within the iddah period nor marry again until the ex-wife marries another man, to ensure that the divorce is taken seriously.

According to the Qur'an, “And if he has divorced her [for the third time], then she is not lawful to him afterward until [after] she marries a husband other than him. And if the latter husband divorces her [or dies], there is no blame upon the woman and her former husband for returning to each other if they think that they can keep [within] the limits of Allah . These are the limits of Allah, which He makes clear to a people who know”. (Al-Baqara 2:230, Shahih International Translation).

Nikah halala cannot be done with the intention of making a woman lawful to her ex-husband. Imam Sufian Sauri explains, "if someone marries a woman to make her halala (for her ex-husband) and then wants to keep her as wife, he is not permitted to do so unless he solemnises a nikah afresh, as the previous nikah was unlawful." However, in spite of considering planned halala to be impermissible, many ulama say "if it is done, the halalah will be valid".

...
Wikipedia