The most common and most likely answer to this crossword clue is the 13 letter word HOUSEBREAKING
I've seen this crossword clue in The Times
H
O
U
S
E
B
R
E
A
K
I
N
G
More clues leading to the result HOUSEBREAKING
Buddy explains!
The straight part
We know that "criminal activity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case criminal activity = housebreaking.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 HOUSEBREAKING mean?
HOUSEBREAKING verb- To train an animal to avoid urinating or defecating in the house, except within a litterbox, toilet, or other receptacle.
- To break into a house, typically to burgle it.
- The act of breaking into another person's house with unlawful intent.