The most common and most likely answer to this crossword clue is the 6 letter word RANSOM
I've seen this crossword clue in The Times
R
A
N
S
O
M
More clues leading to the result RANSOM
- Money demanded from Romans — outrageous
- Wanting drug, smuggled a bit for dirty money
- Sons in manor surprisingly free with money?
- Hurried a bit, nearly producing kidnapper's demand
- Did career thus mark the price of freedom?
- Take Freemason’s money in return for hostages
- US poet’s redemption
- Price demanded to remove top of fanlight in America
- Free, in a way, but it comes at a cost
- Veteran sommelier pocketing pay–off
Buddy explains!

The straight part
We know that "dirty money" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dirty money = ransom.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 RANSOM mean?
RANSOM noun- Money paid for the freeing of a hostage.
- The release of a captive, or of captured property, by payment of a consideration.
- A sum paid for the pardon of some great offence and the discharge of the offender; also, a fine paid in lieu of corporal punishment.
- (14th century) To deliver, especially in context of sin or relevant penalties.
- To pay a price to set someone free from captivity or punishment.
- To exact a ransom for, or a payment on.