The most common and most likely answer to this crossword clue is the 3 plus 5 letter word RAP SHEET
I've seen this crossword clue in The Daily Telegraph
R
A
P
S
H
E
E
T
More clues leading to the result RAP SHEET
- Scoundrel holding the woman in gym is exposed in police account
- One in speech covers list of offences
- Record made by The Police is something covered by Eminem
- Spare the criminal, producing a list of his crimes?
- Knock male in group with criminal record
- Criminal record knocks man
- Blow cover revealing criminal record
- Spare the criminal a list of his crimes
Buddy explains!

The straight part
We know that "criminal record" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case criminal record = rap sheet.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.