Hair Transplant to Facial Scar
Generally, scar tissue has decreased vascularity (blood supply) and thus the survival rate of transplanted grafts in scar tissue is decreased. I have performed many procedures like this with excellent results. I would recommend the FUT/Strip method for this vs the FUE method as grafts obtained via the FUT method are more complete in general as they are microscopically dissected vs blindly punched.
Hair transplant surgery to facial scars can work but only if you grow a beard long enough to cover the scar.
If you are keeping your beard short as you do in the photo, a hair transplant surgery likely will not help.
Scalp MicroPigmentation can work well in these cases.
There are two ways to treat this: (1) a hair transplant will fill in the scar, but leave a white background to the scar even if it is covered with hair. (2) the use of scalp micropigmentation works very well for this, See web reference below
Scar hair transplant
Due to reduced blood circulation to the scar Area there is a 30 percent chance of grafts not to take. However we have done scar tranplant same size as yours in the past and it has been successful, there is a small chance that you may need additional procedures, but in smaller session.