It's best to clarify with your outfitter.
What I've found is if the outfitter mainly caters to US Hunters its pretty common for them to build the VAT into the price and you never have to worry about it. They'll often list that under "included", and have a small asterisk on the trophy fee price list about it for non-exported trophies. Sometimes auction hunts will have it as a "not included" line item.
Conversely I've found outfitters who cater to a lot of European clients normally list it separately. I think it goes back to what
@375Fox said it being pretty standard in Europe and other parts of the world and they're used to it being much higher than US Sales Tax.
Another thing I've found interesting about outfitters and what cultural clients they target is their pricing structure. Since tipping isn't as common in other areas of the world, I've seen some differences between safari outfitters that primarily target European clients vs American clients. I know of at least one South African Outfitter that has an American Price List and a European Price List, but someone like
@Muskox who's been to a bunch of European and American Hunting shows might be able to better comment on that.