The Hydra's fang is an item dropped by hydras and the Alchemical Hydra. It can be combined with the Hydra's eye and heart to create the brimstone ring.
Much like abyssal bludgeons, players will not receive duplicate pieces until they have all three Hydra body parts. For example, if a player has obtained a Hydra's fang, they are guaranteed to get either an eye or heart next time.
A player uses the hydra body parts on each other, turning it into a brimstone ring.
When attempting to create the brimstone ring, a warning will appear in the chatbox stating that the process cannot be reversed, and a confirmation will appear afterwards asking if players would like to proceed with the combination. Should the player confirm, the chatbox will state You successfully combine the Hydra Heart, the Hydra Eye, and the Hydra Fang to create the Brimstone Ring.
For an exhaustive list of all known sources for this item, see here