The most common and most likely answer to this crossword clue is the 7 plus 10 letter word CAPITAL PUNISHMENT
I've seen this crossword clue in The Daily Telegraph
C
A
P
I
T
A
L
P
U
N
I
S
H
M
E
N
T
More clues leading to the result CAPITAL PUNISHMENT
Buddy explains!
The straight part
We know that "HANGING" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hanging = capital punishment.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.