The most common and most likely answer to this crossword clue is the 7 plus 4 letter word CAPTAIN HOOK
I've seen this crossword clue in Independent
C
A
P
T
A
I
N
H
O
O
K
More clues leading to the result CAPTAIN HOOK
Buddy explains!
The straight part
We know that "He single-handedly fought to secure eternal youth" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case he single-handedly fought to secure eternal youth = captain hook.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.