The most common and most likely answer to this crossword clue is the 6 plus 4 plus 2 plus 5 letter word WANTED DEAD OR ALIVE
I've seen this crossword clue in Financial Times
W
A
N
T
E
D
D
E
A
D
O
R
A
L
I
V
E
Buddy explains!
The straight part
We know that "advert devised to catch criminals" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case advert devised to catch criminals = wanted dead or alive.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.