I was wondering: is there in English a specific phrase to denote a music band not playing with its whole current group of members?
Depending on context...
For a small music group such as a rock band, for example, I'd mention the missing current members:
"The legendary Prog-Rock group YES will be touring the US this summer minus its iconic lead vocalist, Jon Anderson."
If it's a large group such as the US Army Band, for example, I might call the smaller group an "ensemble" made up of members from the US Army Band.