Is there a cure for hyperthyroid?

Yes depending. There are also some natural approaches that can be of benefit, but what exactly they are will depend on what exactly is wrong with your thyroid.
Yes. There are three main therapies for the disease -- radioactive iodine (i-131), surgery, or pharmaceuticals -- each of which has its pros and cons. I-131 and surgery are considered cure for the disease. Pharmaceuticals will control the disease but might not cure it in 60-80% of the patients.