Here you can find a build of Spotify for Linux. Spotify team are running this themselves and they will try to make sure it keeps pace with its Mac and Windows siblings. However, this version is unsupported. You can tell them what you think and ask other users for help at The Spotify Community.

Spotify for Linux is released as a Debian package. Their aim is that it should work with the latest Long Term Support release of Ubuntu, but they will try to make it work for other releases of Ubuntu and Debian as well.

Installation

# 1. Add the Spotify repository signing key to be able to verify downloaded packages

sudo apt-key adv –keyserver hkp://keyserver.ubuntu.com:80 –recv-keys BBEBDCB318AD50EC6865090613B00F1FD2C19886

# 2. Add the Spotify repository

echo deb http://repository.spotify.com stable non-free | sudo tee /etc/apt/sources.list.d/spotify.list

# 3. Update list of available packages

sudo apt-get update

# 4. Install Spotify

sudo apt-get install spotify-client

Once you successfully installed it, you may search spotify on your application list.

source: https://www.spotify.com/id/download/linux/