I have fine hair and had an FUE one years ago, can I repeat the transplant to thicken it up? (photo)

Yes, it is not unusual to thicken up the transplant with a second hair transplant, especially people with fine hair. Mechanically, there are limits to how close one can place grafts in a first surgery but on a second surgery, the surgeon goes between the previous grafts and this will double the density.  After the next surgery, you should look good.