The most common and most likely answer to this crossword clue is the 9 letter word PERSUADER
I've seen this crossword clue in Financial Times
P
E
R
S
U
A
D
E
R
More clues leading to the result PERSUADER
Buddy explains!

The straight part
We know that "Convincing one" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case convincing one = persuader.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 PERSUADER mean?
PERSUADER noun- One who, or that which, persuades.
- A tool used to pack the type into the form.