North Cyprus operates a fairly modern state run healthcare system, albeit still a little behind the times in places. However, it is perfectly acceptable for the majority of the population, although expatriates may also prefer to have the addition of private health insurance if they can afford it.
The private healthcare sector in North Cyprus is one which you should feel comfortable about if you are considering relocating to live here. Should you ever need treatment for any number of ailments or illnesses, or require emergency treatment such as surgery, then there are excellent and well equipped facilities to deal with pretty much every eventuality.