The most common and most likely answer to this crossword clue is the 13 letter word IRRESPONSIBLE
I've seen this crossword clue in The Daily Telegraph
I
R
R
E
S
P
O
N
S
I
B
L
E
Buddy explains!
The straight part
We know that "reckless" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case reckless = irresponsible.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 IRRESPONSIBLE mean?
IRRESPONSIBLE noun- Someone who is not responsible.
- Not responsible; exempt from legal responsibility, not to be held accountable.
- Lacking a sense of responsibility; performed or acting as though without responsibility; negligent.