This nicely done old carving showed up missing a few pieces. I always seem to enjoy these repairs.
If the pieces were just broken off and available then in most cases they can be just glued back in place for the most part. But here none of the pieces were available. So the first thing is to prep the broken surfaces to get them flat so new pieces can be added. The easiest way in this case was to use a table saw to produce flat surfaces on the carving. Just position the carving over the table saw and elevate the blade so it just skims the cracked area and leaves a smooth surface. Easy.
It so happens that this carving is symmetrical from side to side so I just made a pattern from the one side to complete the opposite side. Trace the complete section, flip it ,align it with the carving and you can then see the pattern you need to make a new missing section.
The easiest way to carve the missing pieces and induce the least amount of stress on a glued joint or the original fragile carving is to do the majority of the carving prior to gluing it in place. I band sawed the pieces I needed. I then used double sided tape to hold them to a panel and then carved them. It was easy to slide the total carving on and off the panel as I carved to check shape and profiles. At some points I just clamped the carving to the panel where the new pieces were being carved.
Once the forms are established finish the carvings with the style and textures used on the rest of the piece matching it as best you can. Then wrap it up by staining and adjusting the colors as well as the sheen to match the existing carving.