As of the preview event there are no mounts in New World, and it can take quite a bit of time to move around, however, there are some fast travel options available in game.
The first option is by traveling to a settlement (not a fort), and visiting the Inn. Once you visit the Inn you can talk with the Innkeeper and receive the option to gain fast travel to that particular settlement. You can only have one Inn active at a time, so if you travel to another settlement and set that settlement as your fast travel location via the Inn option it overrides the previous Inn you had selected.
Once you have visited an Inn and set it as your fast travel location you can then fast travel back to your selected inn from anywhere in Aeternum. Simply press M to open your map, and click on the settlement you have chosen. You will then see the option to “Recall to Inn.” There is a 1 hour cooldown associated with this option.
Option number 2 is fast travel by using the resource Azoth. Open you map and click on the settlement you wish to travel to. Below the “Recall to Inn” Option there is “Fast Travel” Option. This option costs Azoth, and the cost varies based on distance, encumbrance amount, faction discounts, and guild discounts. You must have enough Azoth, and must have visited a settlement before you can use this option.
Option number 3 is through home ownership. If you own a home within a settlement and are not past due on your taxes then you can use that home as a fast travel location to that particular settlement.