The tattered Kalphite Queen head is an item dropped by the Kalphite Queen. Players are guaranteed to receive one for their 256th Kalphite Queen kill; players who already had 256 kills before the tattered head's release will receive it on their next kill instead.
Like the normal kq head, it can be taken to the taxidermist in Canifis, where she will charge 50,000 coins and turn it into a stuffed tattered kq head. They can then mount it in their player-owned house using 2 mahogany planks and 2 gold leaves, where talking to it is part of the Desert Elite Achievement Diary. However, it cannot be used to create a green slayer helmet, nor can it be sacrificed at the Dark Altar in Arceuus.
When players take it to the Taxidermist, she will say "That's not the most impressive head I've seen but I think I can just about manage this one. Preserving insects is always tricky. I'll have to be careful..."
For an exhaustive list of all known sources for this item, see here