The most common and most likely answer to this crossword clue is the 5 letter word ELVAN
I've seen this crossword clue in The Guardian
E
L
V
A
N
Buddy explains!
The straight part
We know that "Self-willed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case self-willed = elvan.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 ELVAN mean?
ELVAN noun- The rock of an elvan vein, or the vein itself.
- Of or relating to certain veins of feldspathic or porphyritic rock crossing metalliferous veins in the mining districts of Cornwall.
- Elven, elfin, pertaining to elves.