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This is the pommel of King Robert’s sword, and it’s one of the most fantastical pieces of weapon design that originated from the pilot and managed to be used into the rest of the series. We’ve seen it before, and can say it’s a rather long weapon.
The pommel is, of course, a point of discussion. We are fairly certain it’s meant to represent a dragon’s head, given that nose-like indention, but seem think it may be a sort of very stylized kraken. In either case, it’s a war trophy: either taken from the Targaryen armory (or Prince Rhaegar’s corpse?) or from the Greyjoys following their failed rebellion. If it’s a Targaryen weapon in origin, it’s an interesting elaboration on Robert’s personality. His hatred of the Targaryens is famous, and Robert as characterized in the novels largely got rid of things closely connected to them… but one could certainly see room for his carrying a trophy that reminded him (and everyone else) that he put an end to the Targaryen dynasty.