It depends. How long you have lived in Iceland and your circumstances at the time of the divorce can make a difference.

If you have lived in Iceland and held a residence permit for at least two years, you can apply for a renewal of your residence permit on a new basis. You might qualify for a residence permit on the basis of special ties to Iceland. Note that there are further requirements which you must fulfill.

You must apply for renewal on a new basis in order to maintain your residence right. Note that the time you have lived in Iceland will continue to count for time requirements for a permanent residence permit as long as you make sure you apply for a renewal before the residence permit expires.

If you are a victim of domestic abuse, you might meet the requirements for a residence permit on the basis of a special ties to Iceland, even if you do not meet the time requirements. But keep in mind that you will be required to provide documents to support your case.