There are few ways.
1. Open my music tab, and select Artists subcategory.
It will show the list of Artists.
If you click on an Artist Music app will show either a list of albums or list of songs if there you have only one album from this performer.
You can then long-click the artist image on the left and it will start playing all the songs from all the albums, starting from the beginning.
To make sure that it plays continuously you need to slide up the bar that is near the bottom, the one with play/pause button.
It will show the currently playing album artwork and at the bottom there will be "Continuous play" or repeat button.
Clicking it will enable looping of what ever currently is selected, so in our described scenario it will be the artist.
2. Select an artist, next to it will be three dots menu (kebab menu) click and select add to play next.
It will add all the songs from all the albums from this artist to the Next playlist. If you do not enable shuffle it will play them in order (continuously), but no repeat.
3. Select an artist click shuffle button next to it. Once it starts playing, you need to slide up the bar that is near the bottom, the one with play/pause button.
It will show the currently playing album artwork and at the bottom there will be "Continuous play" or repeat button and shuffle buttons. Disable shuffle and enable repeat if you want.