The most common and most likely answer to this crossword clue is the 4 letter word NORN
N
O
R
N
Buddy explains!

The straight part
We know that "Amundsen’s fate" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case amundsen’s fate = norn.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 NORN mean?
NORN verb- To mourn; complain.
- To bring forward; proffer; propose.
- To say; speak; utter; tell.
- To call.