The most common and most likely answer to this crossword clue is the 10 letter word BACKSTREET
I've seen this crossword clue in The Sunday Telegraph
B
A
C
K
S
T
R
E
E
T
Buddy explains!
The straight part
We know that "Illicit" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case illicit = backstreet.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 BACKSTREET mean?
BACKSTREET noun- A usually small and narrow street or alley, especially one in inferior or poorer parts of a city, away from the centre.
- A secret, clandestine or illegal scene.
- Associated with neighborhoods on back streets, often in older neighborhoods, with poorer residents.