Yes, you can cross into Northern Cyprus with a rental, but there are some important rules. When I did it, I made sure to check which companies allow it. For detailed guidance on how to rent a car in Larnaca without credit card and still have the option to cross the border safely, this page was really useful: https://roscarlarnaca.com/. They explain which rentals are allowed, necessary documents, and extra insurance requirements. Personally, it was smooth once I had all the papers ready, and driving around the island felt much more flexible.