The most common and most likely answer to this crossword clue is the 8 letter word CROAKING
I've seen this crossword clue in The Guardian
C
R
O
A
K
I
N
G
Buddy explains!
The straight part
We know that "Going west/Going west" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case going west/going west = croaking.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 CROAKING mean?
CROAKING verb- To make a croak.
- To utter in a low, hoarse voice.
- (of a frog, toad, raven, or various other birds or animals) To make its cry.
- To die.
- To kill someone or something.
- To complain; especially, to grumble; to forebode evil; to utter complaints or forebodings habitually.
- The sound of something that croaks.