The most common and most likely answer to this crossword clue is the 9 letter word ELOQUENCE
I've seen this crossword clue in The Daily Telegraph
E
L
O
Q
U
E
N
C
E
More clues leading to the result ELOQUENCE
- Queen and ELO mad about Conservative’s gift of the gab
- Without question, one clue needs revising — key is good use of language
- Rhetoric of old heartless queen in the Spanish church
- Persuasive speech made by tragic Queen Cleo
- Oddball sequel Coen Brothers ultimately dismissed as blarney
- Rhetoric with nothing much put out by Spain after article there
- New Queen's half in love with this French fluency
- Chess rating to nearly satisfy English facility
- Manipulated Cleo, queen with a silver tongue
- Saying hi to fruit in oratory?
Buddy explains!

The straight part
We know that "Persuasive speech" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case persuasive speech = eloquence.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 ELOQUENCE mean?
ELOQUENCE noun- The quality of artistry and persuasiveness in speech or writing.
- An eloquent utterance.