What is the Islamic legal ruling on divorcing a wife who requests a divorce without a clear reason, and what are the consequences for the husband who divorces her in this situation, knowing that he still feels nostalgic for her despite his engagement to another woman?

If the wife waives her rights, or some of them, in exchange for a divorce, there is no objection to that, and it is considered a khul‘. Seeking divorce without a legitimate shar‘i justification is prohibited. Divorce is permissible if there is a reason for it, and it is disliked if there is no reason. The questioner is advised to stop thinking about the girl who rejected him, and to proceed with marrying a girl of religious commitment and good character.