The most common and most likely answer to this crossword clue is the 8 letter word UNCHASTE
I've seen this crossword clue in Financial Times
U
N
C
H
A
S
T
E
More clues leading to the result UNCHASTE
- Indecent broadcast not followed?
- Launch a steamship that’s partly corrupt
- For brunch, a steak’s somewhat indecent
- Having done it with Sue, can’t make up with husband
- Battered nuts, each scarlet?
- Running free, reportedly having had it?
- Immoral aunt – she’s perverted outside clubs
- Indecent Frenchman’s one caught with urgency
- Pick out some in bunch as terrorists, immoral
- Naughty and not run after, we hear?
Buddy explains!

The straight part
We know that "having had it?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case having had it? = unchaste.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 UNCHASTE mean?
UNCHASTE adjective- Not chaste; not continent