What is the most likely cause of the lack of sharpness in this picture? Taken with a Nikon D3000 and a 55-200 lens at 200mm, 1/320s, f/5.6, ISO 400.
Either the focus was off a little, or the lens if very soft.
To distinguish between these two, take other pictures with the lens at 200 mm, about the same distance, and carefully focused. If they are also soft, then it's the lens. Other than checking to make sure it's really clean with no grease or dust on the front, there is nothing you can do about it.
If the other pictures are nice and sharp, then your focus was off this picture. Take more care next time.
It might depend on how you were tracking focus, auto, single, continuous & whether you had a single AF point or many; also whether your choice would leave the camera in a 'fixed state' between half squeeze & shot, or whether it would still be tracking.
It really just looks like the distance changed slightly between the half-squeeze & the shot.
Auto Focus Continuous [AF-C], 3D would help to avoid that. Centre on the near eye before half-squeeze, then you can reframe before the shot. Even if your subject moves, the 3D ought to maintain focus on that eye.
The focus is not on the face. You can use single point AF and half press to focus on the eye. Then use AF lock button to ensure the focus remains at the same place and recompose to take the picture. Also you can go for a smaller aperture (f8) to increase the depth of field. The background will be blurred anyways at 200mm.