The most common and most likely answer to this crossword clue is the 1 plus 6 plus 4 letter word E STREET BAND
I've seen this crossword clue in Financial Times
E
S
T
R
E
E
T
B
A
N
D
Buddy explains!
The straight part
We know that "Backing group" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case backing group = e street band.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.