In Mirror’s Edge Catalyst, you’ll be able to fast travel to unlocked safe houses. However, you’ll first have to hack the nearby Gridnode in order to unlock that function.
First up, bring up your map and select the safe house that you wish to fast travel to. If it’s locked, the game will tell you that you need to hack the Gridnode. Look around the map for a cross symbol. It should look something like this.
This symbol represents the Gridnode that you need to access and hack before you can fast travel freely to the safe house in that area. Simply head to the Gridnode location, hack it, and that area will now be open to you. After doing so, you can bring up your map, select that safe house, and teleport there.
Do remember that all of the safe houses and different sections of the city are tied to different Gridnodes. If you wish to unlock the fast travel function for all of the safe houses, you’ll have to hack all of the Gridnodes in the game. While running around the city is a quick way to get around in Mirror’s Edge Catalyst, your traveling distances will increase a lot the further you get into the game, so consider hacking the Gridnodes as soon as you unlock them.