Is there a procedure to plump up or fill in this area near my eye? (Photo)

You would be wise to consult with an experienced, board certified cosmetic dermatologist. At least from the one photo provided it would appear that this site can be quite easily plumped and smoothed using a low viscosity, malleable, cohesive HA filler properly injected by a skilled filler injector. This is not an area to be left to the hands of novice, inexperienced injectors trained only to treat ordinary smile lines with plane Restylane or Juvederm. Done properly, treatment should take no more than three to five minutes with immediate on the spot results. Hope this helps and best of luck.

In your case the treatment is quite easy, just about any filler or fat can be used to fill out the small hollow outside of your eyes. I hope this helps and good luck from New York City Plastic Surgery.