iOS 10: Clear 'Up Next' Queue in Apple Music
One workaround to clear the queue and also to play a single song: 


Quit the Music app. This will clear the "Up Next" queue. 
Find the song you want to play alone. 
Tap–hold the song to hail the contextual menu. 
Tap "Play Next". This creates a new queue for the lone song. 
Tap the queue and play the song. 


I admit it's frustrating in that it interrupts music if already playing. And it's unintuitive. 

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