The most common and most likely answer to this crossword clue is the 6 letter word ANOMIE
A
N
O
M
I
E
Buddy explains!

The straight part
We know that "hopelessness" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hopelessness = anomie.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 ANOMIE mean?
ANOMIE noun- Alienation or social instability caused by erosion of standards and values.