To get a "catchlight", which is the term for the reflection of a light in the eyes, you'll need to put a light somewhere that the eye reflects. (Sorry if that seems obvious.) Essentially, this means someplace that the eyes can see.
If your subject is facing the camera, the obvious place for a light is near the camera -- this will create a reflection near the center of the eye. A popular way to do this in portrait and fashion photography is with a ring light -- a light that wraps around the lens. This creates a circular catchlight that will wrap around the subject's pupils if they look directly into the lens. Another way to do this is with a catch card or bounce card, as Gapton points out, or with the on-camera flash. In this case, I think a bounce card will be too high, and be shadowed by your subject's eyelids.
Likewise, a light placed above and to the right of the camera will create a catchlight above and to the right of the center of the eye.
In your case, since your subject is looking down and to the left, you'll probably want to place a light at low camera left. You could also place the light near the camera, and get a catchlight to the right of the pupil. If you place it to the right of your camera, your subject's left (camera right) eye might catch it, but on the outside edge. Chances are, the nose would shadow the other eye, preventing a catchlight from appearing.
Adding a light to create a catchlight will affect the mood of your photograph -- for one, the catchlight "puts a sparkle in your eye", literally speaking, and will convey that emotion onto your subject. Second, the light that creates the catchlight will also light the rest of the face, and may take away the shadow that makes the photograph seem somber and pensive.