Sutherland quit the group with immediate effect last week after claiming that he had found it "impossible" to reform the teetering business.
Barr will continue with her responsibilities, but will now report to Nick Folland, chief external affairs officer, who is adding responsibility for all aspects of membership and social goals into his existing internal and external communications role.
Paula Kerrigan, chief strategy officer, will now become a member of the board, and continue to develop the group’s purpose and strategy.
Interim group chief executive Richard Pennycook will take on a new management executive role of chief operating officer, overseeing finance, IT, risk and transformation delivery once a new chief executive has been found.
Pennycook said: "I am pleased to be announcing these changes to our management team, which mean we are better positioned to tackle the complex issues we face.
"We are focused on the hard work needed to complete the development of our new strategy. This is the right team to deliver that strategy in the interests of all our stakeholders: customers, colleagues and members."
Steve Murrells, chief executive of retail, will maintain responsibility for food, pharmacy, farms and e-store, but will also take responsibility for property and estates.
Rod Bulmer moves from his position of deputy chief executive of the Co-operative Bank to become the chief executive of consumer services. He will join the group in June and become responsible for general insurance, funeralcare and legal services.