The most common and most likely answer to this crossword clue is the 2 plus 4 letter word BY PLAY
B
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More clues leading to the result BY PLAY
Buddy explains!

The straight part
We know that "a bit of action on the side" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a bit of action on the side = 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.
Crossword Answer definitions
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.