Tap on the artist's profile, scroll down, and click “See discography.” The “See discography” button is located underneath the “Popular releases” section right before the “Featuring [artist name]” section. Tapping this will open a page with all the artist's albums and singles available on Spotify.

Just go to artist's page, click on extension icon and click "Show all songs" button. After couple of seconds you will be redirected to new playlist with all songs of this artist.

Did you know there's an easier way to find an artist's radio playlist instead of searching through their Spotify page? Open an artist's page or album, tap the three dots settings button next to the Follow button. On the next page, tap Go to radio and you will be taken to that artist's radio playlist.

Click on artist's header. On the artist's profile page, scroll down to discography.