When you change from one note to another, changing fingering is not enough. You need to accompany this change with your lips as if you where playing on the mouthpiece alone. How big will the movement be will depend on the range and interval. The key to a nice smooth legato is a good coordination between your fingers, lips and air.
You can practice this coordination by playing legato exercises while being aware of the sensation in your embouchure at the same time. You'll then feel where the notes are in your mouthpiece. Practice slow at first and then speed up the tempo until you get a nice, clear and smooth change.
With time, it'll become natural and you won't have to think about it anymore.
I am associate principal horn of the Singapore Symphony Orchestra and the author of the progressive methods. I'm happy to share my experience as a horn player and teacher with you.