All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
You did not mention to us whether or not this woman is from the people of the book, and you did not clarify to us whether this separation took place by divorce and the like, or just staying apart.
Any way, if this woman is not from the people of the book, then your marriage to her is void but if you had any children with her, they will be traced back to you if you married her while believing that this marriage is correct. After making sure that she is not pregnant you may marry her with a new marriage contract fulfilling the conditions of a correct marriage contract, the most important of which are the consent of her guardian and the presence of two witnesses. If she has no Muslim guardian, then she may appoint any Muslim who will marry her off to you. For more benefit, please refer to Fatwa 83629.
However, if this woman is from the people of the book, then your marriage to her was correct if it fulfilled the conditions of a correct marriage contract. If you did not divorce her, then she is still your wife, therefore, you may keep her if she repented. In this case you should treat her kindly and teach her her religion. But if you divorced her and her waiting period finished, then it is an irrevocable divorce, and you are not permitted to marry her except with a new marriage contract. You have the choice whether or not to marry her, but it might be that it is more appropriate for you to marry her if you predominantly believe that she is sincerely a Muslim (and acts according to religious requirements). For more benefit, please refer to Fataawa 90171 and 89050.
Allaah Knows best.