If the two photos were not taken from exactly the same position, a point-based transform usually won’t give a clean match and can introduce odd distortions. In that case, the best approach is usually to match them visually with crop, scale, and rotation rather than forcing exact alignment.

In GIMP, load the old photo as a background/reference layer and place the new photo above it. While using Rotate or other transform tools, you can make alignment easier by adjusting the transform preview opacity in the Tool Options so you can still see the reference underneath. If needed, temporarily hide the upper layer in the layer stack while checking the background reference, then continue adjusting.

You may also need to scale one image first so both are roughly the same size before fine-tuning rotation and crop. If the viewpoints differ, expect to settle for a close visual match rather than a perfect overlay.