She is the president of the Board and as such was the appointing authority for the director who conducted the interviews. There is a close personal relationship between the two. Do I have any recourse?
There isn't generally a civil cause of action for nepotism or conflict of interest for an aggrieved employee. Depending on who the employer is, there might be an internal grievance procedure. Or, if it can be established that there was discrimination against the employee on the basis of a protected status (e.g. sex or gender), there might be recourse for the employee.