If a person commits a crime which deserves a hadd punishment in a land that is not ruled according to that which Allaah has revealed, what is to be done?

The scholars are unanimously agreed that the hadd punishment can only be carried out by the imam (Islamic ruler) or his deputy. This is in the people’s interests and is for the protection of their soul, their wealth and their honour. The imam is able to carry it out because of the power and authority he has, which make the people obey him, and because no one can accuse the imam of being biased or negligent in carrying out the hadd punishments. Thus the imam is able to carry out the hudood punishments in the proper manner so that the shar’i goals will certainly be achieved.  

Al-Mawsoo’ah al-Fiqhiyyah, 17/145.

 It says in Fataawa al-Lajnah al-Daa’imah, 7/21: 

The hadd punishments can only be carried out by a Muslim ruler or one who takes the place of the ruler. It is not permissible for individual Muslims to carry out the hadd punishments because of the chaos and fitnah (tribulation) to which that will lead.”  It also says (21/5-6): 

No one can carry out the hadd punishments except the Muslim ruler or his deputy, in order to maintain order and prevent anyone from transgressing against others, and to protect against injustice. And the sinner has to pray for forgiveness and repent to Allaah and do a lot of good deeds. If he is sincere in his repentance towards Allaah, Allaah will accept his repentance and forgive Him by His grace and kindness. Allaah says (interpretation of the meaning): 

“And those who invoke not any other ilaah (god) along with Allaah, nor kill such person as Allaah has forbidden, except for just cause, nor commit illegal sexual intercourse and whoever does this shall receive the punishment.

69. The torment will be doubled to him on the Day of Resurrection, and he will abide therein in disgrace;

70. Except those who repent and believe (in Islamic Monotheism), and do righteous deeds; for those, Allaah will change their sins into good deeds, and Allaah is Oft‑Forgiving, Most Merciful” [al-Furqaan 25:67-70] 

“And verily, I am indeed forgiving to him who repents, believes (in My Oneness, and associates none in worship with Me) and does righteous good deeds, and then remains constant in doing them (till his death)” [Ta-Ha 20:82]

And the Prophet (peace and blessings of Allaah be upon him) said: “Islam erases whatever came before it, and repentance erases whatever came before it.”.