The Exeter-based healthcare and protection insurer has created the role to head up its pricing and actuarial function.
Andy Chapman, chief executive officer, said: "I'm delighted to welcome David to Exeter Family.
"His ability and considerable experience will make him a huge asset to our team going forward."
Cobley is a fellow of the Institute and Faculty of Actuaries.
He joins from Simplyhealth where he was commercial director, while previously he worked within Lloyds Banking Group and Legal and General Insurance.
Cobley added: "I'm delighted to be joining a thriving organisation with such ambitious growth plans."