Typically lots of people owe a duty of care to any individual in modern society. But it is hard to see that anyone would owe a duty of care to councillors in the specific way described. The test of whether conduct could be reasonably foreseen to involve harm would be difficult to meet. Usually, the harm is pretty obvious, such as a car that puts its occupants at risk of physical injury.
Having said that, a successful council is likely to encourage all its members, and to particularly aim to assist new members to carry out their responsibilities effectively. Not all councils have problems of this kind. Although there are support organisations such as the National Association of Local Councils, they are typically aimed at supporting the council as a whole, and may not be accessible to individual councils.
The best option may be to encourage sympathetic councillors to provide support and to help new councillors to resist any unreasonable pressure from any source. This site was created in response to the limited opportunities for councillors to find support and to help one another, or to receive helpful advice from clerks offering goodwill.
