If you use a graduated filter, colored filter, or any filter that isn't completely clear, it will affect your exposure. As the others have mentioned, the camera will compensate and still evaluate the exposure with the filter in place. What will happen, however, is that something will change--either your aperture, shutter speed, or ISO--depending upon which mode you are using (Aperture Priority, Shutter Priority, Manual, or if you have auto-ISO enabled).
Perhaps that's what you meant when you asking about changing the aperture. It is one way for the camera to compensate. For example, if you are in shutter priority, the camera might alter the aperture to correctly expose the image. It all depends upon what settings you are using.
If you use an ND filter that has a hard line (as opposed to a graduated ND filter), then you will want to use a wider aperture. In those instances, if you are using an ND filter with the hard line, it will be visible when shooting stopped down. That would be a time when you'd need to adjust your aperture wider (open it up more).