Getting Spotify for Apple Watch is simple. You just need a few things:
When you’ve got those things, the Spotify for Apple Watch app will be automatically installed onto your Watch (remember, Apple Watch apps are added to the Watch after they’re installed on the paired iPhone). If it’s not, try restarting your iPhone and it should appear on your Watch.
The Spotify app not showing up on your Apple Watch? It might be good to refresh yourself on how to install apps on the Apple Watch.