Could I achieve a thicker beard with a beard hair transplant? (Photo)

A beard-hair transplant can certainly thicken your beard hair volume. I encourage you to research different techniques from different surgeons in order to find the one that suits you best. It is very important to understand every step of your procedure from extraction to graft preparation to implantation. Some surgeons may create loopholes in the graft preparation process. 
Aside from transplantation, you may want to consider trying a Platelet-Rich Plasma (PRP) injection first. The addition of concentrated growth factors to thinner regions of hair can drastically stimulate follicle growth. Plus, it's a financially conservative treatment. I like to use PRP with my patient's hair transplants, as well as separately from their procedures. Patients that have thin regions of hair can use PRP for correction to hair density and there are numerous areas you can use it - beard, brows, and scalp being most common.
Best, 
Anil Shah, MD

Yes, a beard transplant would help you achieve the density you desire.  Beard and mustache transplants are becoming more popular.  You should have a consult with a hair transplant surgeon that is an expert in hair transplant to the face.

The beard transplant is the ideal solution when the beard is not dense enough, presents holes in its hairiness, is too low, when you want to conceal imperfections like scars or simply harmonize the features of the bottom of your face. We use the FUE technique for beard implants which is the technique used for the implant of the bristles in order to leave no scar..
The rate of the beard Transplant is around 90% if it is performed by a specialist surgeon.