Is the secret marriage of a divorced sister to her ex-husband's brother, she being a committed and truly repentant woman, permissible or forbidden?

A legitimate marriage fulfills the conditions for its validity, such as the guardian's permission and the presence of witnesses. It is what makes it permissible for a man and a woman to cohabit. As for a mere agreement between them, it is not a legitimate marriage; rather, it is zina (fornication/adultery), and they must repent from it. If they desire to marry, he must propose to her through her guardian and conclude a legitimate marriage contract with her. Otherwise, they must separate, because mukhadana (taking mistresses) is forbidden.