A council member can be the clerk, but cannot be paid (including for a period of 12 months after ceasing to be a councillor).
The clerk can use whatever resources may be available (paid or unpaid) to get the job done. Although I guess one should be careful to ensure that if reliance is placed on an external person, they somehow have a duty of care in relation to the work. Also, there's always a risk of someone who does work for the council becoming a de facto employee. But worrying about that may be ultra cautious.