The most common and most likely answer to this crossword clue is the 5 letter word TOMMY
I've seen this crossword clue in The Daily Telegraph
T
O
M
M
Y
Buddy explains!

The straight part
We know that "Private soldier/rock opera" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case private soldier/rock opera = tommy.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.
What does TOMMY mean?
TOMMY noun- Bread, generally a penny roll; the supply of food carried by workmen as their daily allowance
- A truck, or barter; the exchange of labour for goods instead of money.
- To pay (employees) according to the truck system, with goods instead of money.