The most common and most likely answer to this crossword clue is the 4 plus 3 letter word SPIN OFF
I've seen this crossword clue in The Daily Telegraph
S
P
I
N
O
F
F
Buddy explains!

The straight part
We know that "By-product" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case by-product = spin off.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 SPIN OFF mean?
SPIN OFF noun- An offshoot.
- An incidental benefit or unexpected pay-off.
- By-product.
- A fictional work where the protagonist was introduced in a preceding work or at least shares the same setting, often in a different aspect.
- The formation of a subsidiary company that continues the operations of part of the parent company; the company so formed.