The decision on how to fill the vacancy must be taken at a meeting of the Council or of a duly delegated committee. If your Council has adopted employment policies or procedures, these must be followed. If not, there is some discretion for the Council with regard to the mechanism to be employed, however wider legislation such as Equality Act may have a bearing too.
A vacancy is a good opportunity to pause and consider the clerkship arrangements, review the hours, pay grade, conditions of service, contract of employment etc.
Who made the decision and how will it be recorded in the official records of the Council? I trust that the Vice Chair had no involvement!