A lot of nonprofits have executive directors without referencing the position in the bylaws of the corporation.  The executive director tends to function as a chief executive officer with full signing authority delegated explicitly or implicitly by the board.   Obviously it is a much better practice to spell out the range of authority in a board resolution. But the title itself creates “apparent authority” to act on behalf of the organization, and outsiders who have no reason to know of any limitation are generally able to rely on such apparent authority to bind the organization.  If you don’t want to give your executive director authority to act on behalf of the organization, you probably ought to change her title.

By the way, it is somewhat unusual to treat an executive director as an independent contractor rather than as an employee.  Unless she is not working for you full time and it is clear that she is doing the same kind of work for other organizations, or at least holding herself out as being able to do so, the IRS is likely treat her as an employee and look for your withholding tax returns.