This person woud have been a member of the Churchwardens committee or parish Council, whose responsibilities covered all aspects that any local authority would cover, including some minor offences, serious matters were dealt with by the local magistrate,
I supervisor of the highways would be responsible to the accuracy and maintenance of any mile stones, for ensuring that all roads leading into and out of and through the town were passable, probably not on wet muddy days, but there would be cinders gathered and laid down to mprove the passage of wagons and carts, the supervisor may also have been responsible for the marking of the parish boundary, which was extremely importnat as during thie period the Act of Settlement could only be enforced if people could distinmguish in which parish they had a right of settlement. there was a tradition of beating the parish boundary, which in some villages allegedly involved marking the boundary by holding a child upside down and banging their head on the ground deemed to be the boundary, lol sounds dafr don;t it?
Any expenses would be paid from the parish coffers, from the Patish Rates, the job would be voluntary and probably a new person was elected every year, Parish's varied, the role would be taken by someone who had no need to work but was living on their own means or had an income from property or an estate, sometimes it might be a local yoeman farmer or tradesman, the expenses would be written up by the Parish Clerk and presented at the Council meeetings and recorded in the minutes, the expenses can sometimes be found in the Parish papers surtviving in County Record Offices where the Diocesan Office or the parish has deposited them.