In what I'll call "Classic" Spotify it was possible to select, say, the first five tracks of a ten track album (click on the first track, then SHIFT-click on the fifth track), then right-click on a song from that selection, after which you'd click Play from the context menu and those five selected songs (and those five selected songs only) would play.
If you try that in "New" Spotify you'll find that nothing happens when you click Play.
Interestingly other "actions", such as Add to Playlist, will operate on that subset of songs, but not Play.
Why would do I want to see this restored? Sometimes original release albums are not available, but re-release albums (containing extra bonus tracks at the end) are available. I like to play the original songs only using the method above. Another reason, let's say you have a album where you like every other song on it, the method above would allow you to play those favoured songs without having to click skip at the end of each song.
At the moment the workaround is to create a new playlist with your selected songs and then play that playlist.
Another alternative would be to be able to drag the songs you want to play on the Play Queue - but I've never been able to quite work out the logic behind the play queue (some songs you can delete, others you can't - yada, yada)
This idea has been submitted more than 1 year ago but unfortunately hasn't gained enough kudos during that time (10 kudos/year). In order to keep an overview of the active ideas in this forum, this idea will be closed for now. Note that this does not mean the idea has been declined by Spotify.
Please feel free to re-post this idea if you still feel you want this implemented. With a little change in presentation, maybe this time it will gain the necessary support from the community.