The most common and most likely answer to this crossword clue is the 8 letter word CONVINCE
I've seen this crossword clue in The Daily Telegraph
C
O
N
V
I
N
C
E
Buddy explains!

The straight part
We know that "Persuade" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case persuade = convince.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 CONVINCE mean?
CONVINCE verb- To make someone believe, or feel sure about something, especially by using logic, argument or evidence.
- To persuade.
- To overcome, conquer, vanquish.
- To confute; to prove wrong.
- To prove guilty; to convict.