The most common and most likely answer to this crossword clue is the 6 letter word BYPLAY
B
Y
P
L
A
Y
Buddy explains!

The straight part
We know that "incidental activity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case incidental activity = byplay.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 BYPLAY mean?
BYPLAY noun- Any action, carried out onstage during a performance, apart from the main action.
- Any action, by supporting actor.