In the summer we went through the painful process of removing our chairman from office. It was because of his autocratic style and undemocratic behaviour both at meetings and between meetings.
The head voted against the majority and the teacher governors abstained, I think out of embarrassment because of the head's position: privately they agreed with us.
There was an unduly close relationship between the chairman and head, sewing everything up beforehand, manipulating the rest of us, and assuming our agreement to decisions between meetings. We took the step we did over a decision made by the head and chairman which we objected to.
Now here's the problem. The former chairman is still a governor and even tried to put himself forward again, proposed by the head but lacking a seconder. He is undermining the new chairman and making his job impossible by guerrilla tactics, rudeness and disloyalty outside the school.
Can we get rid of him?
You certainly have a bad governor who totally lacks team spirit. Your headteacher has been extremely unwise to encourage him.
But while, as you know, there is a legal process for voting out a chairman, there is none for voting a governor off the governing body. An appointed governor, that is, LEA or foundation, can be removed by the appointing body for good reason, but it is their decision, and elected or co-opted governors can't be removed at all unless they become ineligible through criminal conviction, bankruptcy or non-attendance.
Despite cases like yours, which are rare, I still think this is right, because I believe more good than bad governors would be at risk of being removed if it were easy to vote people off.
Group discipline is your only hope. You must not let any disloyalty pass without comment, for a start. All must support your chairman in running the meeting smoothly and pleasantly; do not remain silent in the face of rudeness or unkindness.
Above all, if the situation is as bad as you describe, your chairman must on behalf of all of you tell the head how destructive his support of this man is, because this is the key. In fact the head himself is guilty of disloyalty to the team too as he is a governor and is frustrating majority wishes in what should be corporate solidarity. No good can come of this and in the end the school will suffer.
I should add two things. First, there is nothing to stop your passing votes of censure on the former chairman or even saying you think he should resign, though in the end he is not required to take any notice. Second, decisions made by head and chairman without the governors' express agreement are not legal decisions and could be challenged by any injured party.
Your head should be aware that he is running grave risks by not respecting the governors' corporate power.