The chair of a meeting can vote as an ordinary member of the council and, if there is a tie, has a casting vote.
However, it’s important to note that there is no provision in legislation for no confidence motions at parish council level. Unlike in principal authorities, where such motions can trigger leadership changes, a no-confidence motion in a parish council has no legal effect unless the council’s standing orders explicitly provide for it - which is highly unlikely. The motion does not remove the chair from their position or force any action.
Given this, it is questionable whether the clerk should have accepted the motion at all. Clerks have a duty to ensure that motions brought before the council are lawful and within the council’s powers. If a motion has no legal standing and cannot result in any concrete action, its inclusion on the agenda could be considered unwise, particularly if it appears vexatious or politically motivated.
That said, if the motion is debated, the chair remains a full voting member of the council and is entitled to vote against it. If the vote is tied, the chair has a casting vote and may use it, just as they would for any other tied vote. While some may argue that abstaining would be the more diplomatic approach, there is no legal or procedural reason why the chair cannot vote to defend their position, especially against a motion with no legal weight.