With the new aspect ratio on the new 11 inch iPad Pro Spotify currently doesn't take full advantage of the bigger display. It shows big black bars all around making the user interface even smaller than on the previous generation iPad Pro. I would love to see an optimized version of the app since I have always been a big fan of the Spotify UI on mobile devices.
Updated on 2019-03-25
It sounds like this got fixed and the Spotify app now appears in full screen on iPad Pro 11".
If it's still appearing small on your device, giving Spotify a quick reinstall should fix things up.