If you're ready to make the switch, you can download the Spotify beta here. If you're already running Spotify, you'll need to delete the current version of the app from your PC before installing the Arm64 version. Specifically, Spotify says you may be unable to play certain video podcasts, but for now, you can work around this by using the Share button to copy a link to the episode and watching it on the web instead.
The current version is only available in beta and that means there are bound to be some issues. Spotify is probably one of the biggest names to start catering to Arm64 Windows devices, such as Microsoft's own Surface Pro X.