The most common and most likely answer to this crossword clue is the 7 letter word CODICIL
I've seen this crossword clue in The Daily Telegraph
C
O
D
I
C
I
L
More clues leading to the result CODICIL
- An appendix to one’s Old Testament?
- Feature of will — something fishy, not quite licit, on reflection?
- Will supplement of fish oil initially improve capacity for love?
- Will’s appendage bones looped over, having chip on one length
- Incomplete legal document, in Word, rejected as legal document
- Will’s rider upset detectives, breaking wind
- A note added willingly
- Will supplement from fish get old chemical company money?
- Something fishy and not quite legal about supplement
- A willing rider
Buddy explains!

The straight part
We know that "A willing rider" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a willing rider = codicil.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 CODICIL mean?
CODICIL noun- An addition or supplement that explains, modifies, or revokes a will or part of one.