If it is a paid job your colleague could not legally be chair, for a start. And any decision on the appointment would be yours as a governing body, not the head's alone. If your chair were happy to become and remain an ordinary governor in order to be able to accept the post, or if it were unpaid and seen as an honorary position, it would still be for you to decide whether it was what you wanted, and you might look at the risk of undue influence, given his closeness to the head combined with the standing of a governor.
It is, in my view, essential that decisions about money are made by the governing body or its duly elected finance committee and not by any one person: the expert's job is to make decisions easier for others to make, not to make them. With this caution it might work very well.
My child attends a Roman Catholic school which I chose for its good academic standards and discipline. We have no religious affiliation. On special days all the pupils go into the church for a service in place of the usual assembly, and it is of a very formal and fundamental character. I do not wish my child to participate in such an extreme form of Catholic ritual.
However, the head asked the priest - who is chairman of the governors - to see me. He said if I had chosen a Catholic school my child should conform. What are my rights?
Your rights are total. Any child may be withdrawn from RE or worship at the parents' request, and this applies in an aided school just the same as any other. Nor can it be a condition of entry to such a school that the child attends any place of worship though, of course, it is open to the governors of an aided school to give preference to parents of their own faith in admitting pupils.
So your priest is not correct. It may be a problem for a denominational school to have pupils who do not participate in everything, but the law is clear.