The most common and most likely answer to this crossword clue is the 7 letter word BY-PLAY
I've seen this crossword clue in Independent
B
Y
-
P
L
A
Y
Buddy explains!
The straight part
We know that "secondary activity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case secondary activity = by-play.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 BY-PLAY mean?
BY-PLAY noun- Action carried on aside, commonly in dumb show, while the main action proceeds; action not intended to be observed by some of the persons present.