The most common and most likely answer to this crossword clue is the 4 plus 4 letter word HELL BENT
I've seen this crossword clue in The Daily Telegraph
H
E
L
L
B
E
N
T
More clues leading to the result HELL BENT
Buddy explains!
The straight part
We know that "Recklessly determined" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case recklessly determined = hell bent.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 HELL BENT mean?
HELL BENT adjective- Recklessly determined to do or achieve something