The Star Trek galaxy is a vast universe! Part of the fun is exploring it with your ships!
Hostile ships are found roaming around in the System map. They have many different names but all of of them will have a red label! The number to the left of a hostile ship indicates the level of that ship. For example, this Rigellian Destroyer hostile ship is level 2.
Once you've conquered your starting system, Tap the circular Galaxy button on the bottom right of your screen when you’re on the System map to access the Galaxy map.
Level 3 hostile ships can be found in level 2-4 Systems. A System’s level is displayed next to its name in Galaxy view. A hostile ship of a specific level can be found in a System whose level is +/- 1 from the hostile ship’s level. In the image below, you can expect to find level 1-3 hostile ships in the level 2 Groshi System.