I'm guessing you want to use the NPC transport to go from a starport to another? I'm guessing you are also on a homeworld and at the NPC owned startport.
So go into the starport, and head upstairs to the docking bay. Click the [Actions] button on the HUD and choose the spacetravel option. You should then get a list of starports you can travel to. Choose the one you want and click the button.