Is there a relation between high arched palate and cardiology?

Maybe: There is a theory that a narrow arched palate can not allow room for the tongue while sleeping which then can result in obstructive sleep apnea reducing oxygenation to the heart and brain which relates to cardiology. A sleep test would give you an answer.

Possible: There are conditions that cause a high arched palate that are associated with cardiac disease. The most notable of such conditions is Marfan's syndrome which is associated with aortic aneurysm, valve disease and heart failure.