How can an unveiled, married, expatriate woman who has had a relationship with another man repent?

Allah commanded women to wear the hijab (definition) because it is an obligation that protects women and society, and a Muslim woman does not have a choice in this matter. A forbidden relationship is a grave sin, but Allah is Most Merciful; He accepts the repentance of a servant no matter how great their sin. In fact, He loves those who repent and transforms their bad deeds into good ones, for the one who repents from a sin is like one who never committed it. Repentance is achieved by abandoning the sin, regretting having committed it, resolving not to return to it, and avoiding the causes of disobedience.