Neb. Rev. Stat. § 23-3590

Any vacancy upon the board of trustees, occurring other than by the expiration of a term, shall be filled by appointment by the remaining members of the board of trustees. Any person appointed to fill such vacancy shall serve for the remainder of the unexpired term. There shall at all times be one or more members of the board of trustees who are consumers of health care services as distinguished from providers of health care services.