This desk was also on display at the Hollywood Entertainment Museum until 2008ish, amongst a bunch of pieces of Picard’s office. I’d grab photos if I could at the moment.

It being an ashtray/container of sorts for cigars, makes me think it would make a decent incense holder, and that’s what I presume it’s use might be. Though it also doesn’t seem particularly of the teachings of Surak to use the skull of an animal as an ashtray 😅