Yes. The inclusion of water always means you need a preservative unless the product is intended for immediate use. You will also need to incorporate an emulsifier in order to properly incorporate that ingredient into the rest of the product.
So, to recap, if you want to add something that contains water to an anhydrous preservative, you need to add:
- The new ingredient
- A suitable emulsifier
- A suitable preservative
This is often more trouble than it is worth, so I’d recommend seeing if there is a water-free way to incorporate the ingredient you’re trying to add to the formula. If it’s a tincture, consider an oil infusion instead—that sort of thing.