The most common and most likely answer to this crossword clue is the 15 letter word EXTRACURRICULAR
I've seen this crossword clue in The Guardian
E
X
T
R
A
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More clues leading to the result EXTRACURRICULAR
Buddy explains!
The straight part
We know that "Kind of activity involving adultery" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kind of activity involving adultery = extracurricular.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 EXTRACURRICULAR mean?
EXTRACURRICULAR noun- An activity outside the normal academic curriculum.
- An activity beyond official duties of a job or profession.
- An extramarital affair.
- Outside of the normal curriculum of an educational establishment
- Similarly outside of the normal duties of a job or profession
- Extramarital