This is the kind of situation which businesses often handle with a ruthlessness that does not come easily to the teaching profession. It is, of course, a matter for the governing body, not the head, although you will have to implement whatever policy they decide to adopt.
Their choice is simple: unless they can persuade the education authority to help them out, they have either to find the additional staff costs from their budget, or embark on a programme of redundancies to achieve the target they set themselves. The target should be a staffing structure, commensurate with the size of the school, which meets the structural requirements agreed between the governors and the head. This then becomes the framework within which redundancies may be made and any necessary recruitment is planned.
In planning for possible redundancies, you will need to establish clear criteria, which are likely to be based firstly on curriculum requirements and secondly on costs. In the latter connection, it is helpful to know that budgetary constraint is an acceptable criterion for redundancy, provided that it is fairly applied.
If the governors decide that they can meet the cost of retaining staff, you should ensure that they are given duties which match their salaries.