The answer to your question is that this depends in part on how the pregnancy goes and also, in part, on the hospital or clinic environment where you receive care. Perinatologists, or maternal fetal medicine specialists, are OB GYN doctors
who have received additional training in the management of higher risk pregnancies. Your pregnancy will qualify as higher risk because of the history of an incompetent cervix and the need for a cervical cerclage.
In some hospitals or clinics, the maternal fetal medicine specialist works closely in consultation with the regular OB GYN doctors. In this setting, they may mostly provide additional advice and support, while relying on your regular OB GYN doctor to provide most of the care and also to deliver the baby. Howver, in some other settings, the maternal fetal medicine specialist may take over care of the pregnancy completely, including the delivery.
Therefore, in order to get a definitive answer to your question, I would advise you to sit down and talk with your regular OB GYN doctor to see what they think and what they view their role to be during the pregnancy. You can ask similar questions when you see the perinatologist as well.