1. Get a contingency plan in place
If the search for a new chair or vice-chair is going to take longer than expected, you'll need a plan to continue operating.
If the role of chair is vacant but you have a vice-chair in place, then the vice-chair can deputise for the chair while the search is on. You can read more about that in this article.
If you're searching for a new vice-chair, you might ask governors to rotate through the role on a month-by-month basis until the seat is filled. This has the added benefit of giving more governors some leadership experience and improving any future succession plans.