Carter joined the mutual on 4 July from HSBC Private Bank where he was chief operating officer for nearly three years.
In his role he will oversee day-to-day operations and transformational change at the mutual.
Carter had worked at HSBC in various senior roles since 2013, including around a year as chief administration officer. Before that he worked at RBS Wealth for around six years.
Colin Fyfe, chief executive of Hinckley and Rugby said: “I am delighted to welcome Barry to the society and excited to see what he can bring to the business. He has gathered the knowledge, skills and experience throughout his career to support us in developing our exciting transformation and enable us to continue to provide a high standard of service to our customers.
“As chief operating officer, I am sure that our members and colleagues are at the forefront of his thoughts, ensuring we continue to put people first.”
Carter added that it was a privilege to join the society as chief operating officer. He continued: “I am joining at an exciting time as the society looks to streamline its mortgage process, take steps forward in its digital presence and continue its improvement of day-to-day performance.”