The most common and most likely answer to this crossword clue is the 8 letter word BEQUEATH
I've seen this crossword clue in The Daily Telegraph
B
E
Q
U
E
A
T
H
More clues leading to the result BEQUEATH
Buddy explains!

The straight part
We know that "Leave willingly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case leave willingly = bequeath.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 BEQUEATH mean?
BEQUEATH verb- To give or leave by will; to give by testament.
- To hand down; to transmit.
- To give; to offer; to commit.