A clerk is an employee of the council and the terms and conditions are set by the council. Any change must be agreed by the council, which can only be done in a properly constituted meeting. (Except in the unlikely event that the council had previously resolved to delegate to the clerk the setting of their own terms and conditions).
As usual, a decision requires a clear agenda item, published three clear days in advance, followed by a council (or council committee) decision which must be minuted.
The chairman (or any other councillor) has no power to make decisions of this kind on their own.
The only factor I can think of that would make the situation different would be if the council had agreed to pay the clerk's expenses and had agreed a method of calculation, which could be applied by the clerk, with a different figure resulting from changed circumstances. It is conceivable (but would be reckless) for the council to have agreed to pay whatever the clerk chose to claim, but this would still have required a council decision at some point.
The way forward is to ask what council resolution authorised the revised payment.
