The most common and most likely answer to this crossword clue is the 4 letter word THUG
I've seen this crossword clue in The Times
T
H
U
G
More clues leading to the result THUG
- He could be tough, lacking love?
- Yank arresting first of hoodlums, ruffian
- Tip from agent to stay close to violent criminal [4]
- Yank apprehends hard criminal
- Time to embrace ruffian
- Yank throttling husband is ruffian
- Something in the middle to cling to, tough
- Heavy Yank scoffing the last of goulash
- Ruffian seen in jacket, huge
- Is one awfully tough, without love?
Buddy explains!

The straight part
We know that "criminal" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case criminal = thug.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 THUG mean?
THUG noun- Someone with an intimidating and unseemly appearance and mannerisms, who treats others violently and roughly, often for hire.
- One of a band of assassins formerly active in northern India who worshipped Kali and offered their victims to her.
- In gardening, an over-vigorous plant that spreads and dominates the flowerbed.
- A punk; a hoodlum; a hooligan.
- To commit acts of thuggery, to live the life of a thug, or to dress and act in a manner reminiscent of someone who does.