A To answer your last question, a governing body can certainly function legally with vacancies.
But having said that it is indeed a very sad and worrying situation. I am sure you will in time prove that you are different from your predecessor, but I don't think it wise to wait that long.
If I were you I should meet the whole staff to talk about this. Assure them that you want the staff to be strongly and fearlessly represented, and will in every way encourage the elected teachers to bring staff concerns to the governing body. Promise to see that issues affecting teachers are fairly dealt with. Stress how important teacher governors' contribution to curriculum discussion can be if they contribute without fear, and say explicitly that you would never take any teacher governor's contribution amiss even if you didn't agree with it, but on the contrary would be proud that they felt able to speak up. You might add that OFSTED inspectors would probably be concerned if there were no teacher governors.
If you succeed in getting representatives, you can soon prove your sincerity by encouraging them to speak, serve on key committees and generally play an active part. You might suggest that the governing body has a slot on the agenda for a staff report and that both the teacher governors and other teachers have an opportunity to speak in turn on curriculum issues at governors' meetings to familiarise governors with the work of the school.
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