The existing weapons of New World are nothing short of incredibly interesting, but the worldbuilding of the game has left enough space for others to be added. So, based on some media of the game, we can deduce what those weapons are.
There are four categories of Weapons in New World: One-handed weapons, two-handed weapons, ranged weapons, and magical weapons.
Starting off we have the one-handed weapons. These are currently the usual fantasy weapons of rapiers, swords, shields, and hatchets. However, flintlock pistols may fall into this category, as well as into the shared one. Via data mining, players have found pistols to be mentioned in certain lines of the game. They will certainly come in handy as an off-hand weapon.
The two-handed weapons currently in the game are the spears, axes, and war hammers, the historian in me is in pain typing the last one out though. Nevertheless, we may expect greatswords to be added into the mix. Should it follow the great ax route, it may prove to be very powerful in PvP.
The ranged weapons, currently consisting of muskets and bows, will get an addition as well. Besides the pistols mentioned earlier, the new weapon may be the blunderbuss. One may see the blunderbuss as a time-adequate version of a shotgun, and nothing more needs to be said, really. Perhaps the weapon will have a cone-like hitbox when firing, though the range should leave something to be desired.
As for the magic items, we may expect an earth staff to join the mix. Now, when magic is involved, one can hardly say what we can expect from it, but following the theme, it should be more of a supporting item, just like the Life Staff, but more focused on buffing
Especially so since a lightning gauntlet is expected, and lightning will surely be an offensive element. It must be said though that some rumors have surfaced that the lightning element item will be a scythe, but that is neither here nor there, so we will stick with the gauntlet for now in our calculations.