The answer to your final question is a clear no: it is virtually impossible to remove elected or co-opted governors except for bankruptcy, criminal conviction or non-attendance. You may think you are friendly and a good team, but the evidence is against you. It sounds as though you may all have got so used to being cosy that new governors found it hard to establish themselves.
The induction of new governors should be planned, with head and chair welcoming them and briefing them a little, with another governor asking them to tea or coffee, offering to go to the first meeting or training with them, lend them a book, etc.
You should do everything possible to introduce yourselves at their first meeting; find out a little about them and get them on board as quickly as possible. At meetings you should all take responsibility to explain things and bring them into the discussion. It can be very daunting to join a body which is so settled, not knowing the names or roles, jargon or in-jokes. You should also ensure that whatever work-sharing arrangements you have are extended to them, with help initially if they need it.
If I have done you an injustice and you have attempted all these things, with the new governors remaining unresponsive, it is still more your responsibility as an established group to repair the situation than that of the newcomers. You must, in that case, take steps to enforce in the gentlest way a culture of participation upon them.
All groups have their own disciplinary mechanisms. With governors, it is the example given by a committed team with high expectations of each other. You must assume every day that they want to be useful members and keep on giving them opportunities.
You say you were a good team before so I assume you shared the work, were loyal to each other, expected equal contributions from all, and had some system of regular involvement in the school which everyone had agreed to. All this must be explained to each new recruit and space made for them to join in. There's no need to lecture or be heavy about it, just expect everybody to want to be as involved as the rest.
One does occasionally get a governor who wants the name and not the game, or one who has totally misunderstood the commitment required, but even these, given that they can't be sacked, can best be persuaded to call it a day by gentle pressures which they feel more and more uncomfortable resisting. I doubt very much whether your colleagues are in this category. They are probably just despairing of ever getting into the swim.
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