The most common and most likely answer to this crossword clue is the 4 plus 8 letter word BODY SNATCHER
I've seen this crossword clue in The Times
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Buddy explains!
The straight part
We know that "old criminal" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old criminal = body snatcher.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
BODY SNATCHER noun- One who makes arrests, such as a bailiff or policeman.
- One who abducts or controls another's body, such as a slaver, psychic, or human resources agent.
- One who sells cadavers to anatomists, surgeons, etc., especially by exhuming corpses from graves, a resurrection man.
- (in particular) A graverobber who steals bodies or body parts.