A combination of in office dental bleaching as well as at home bleaching trays should do the job. Zoom is made to work with inside the tooth and get you some results. Individual results vary, but there will be some improvement.
The space in which you describe and the photo shows is commonly called "the black triangle." As stated by another dentist, this is sometime difficult to predict whether or not the gums will fill in the space. Giving it some time will allow us to see if it resolves or if it is something that will remain. Factors that may determine whether remaking the veneer are: 1) Size of the original tooth and how much space did the dentist have to close... The smaller the tooth and the more space, the more difficult it is to improve the gum line 2) Anatomy (or shape) of the veneer... If you're happy with the esthetics or look of the current tooth (excluding the gum issue), then remaking the veneer has some considerations that you will need to decide whether it is worth replacing it. For the dentist or lab to close the gum space, the new veneer would have to be slightly more square-shaped to close the space.