How can one repent from intentional killing motivated by revenge, especially if this occurs in a country where the law is not applied, and the revenge came after the family of the first victim did not receive justice from the killer?

The repentance of a killer is achieved through remorse, seeking forgiveness, and seeking absolution if the killing was unjust. Allah accepts sincere repentance, as stated in His Almighty saying: "Except for those who repent, believe and do righteous deeds. For them Allah will replace their evil deeds with good ones. And Allah is Forgiving and Merciful." However, if a person kills a killer whose blood is not inviolable (i.e., not protected by Islamic law), then he is disobedient for usurping the authority of the ruler. He is not subject to retribution (qisas), nor is he obligated to pay blood money (diyah) or expiation (kaffarah). The ruler will punish him as deemed appropriate.