The most common and most likely answer to this crossword clue is the 13 letter word PRONUNCIATION
I've seen this crossword clue in The Guardian
P
R
O
N
U
N
C
I
A
T
I
O
N
Buddy explains!
The straight part
We know that "a manner of speaking" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a manner of speaking = pronunciation.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 PRONUNCIATION mean?
PRONUNCIATION noun- The formal or informal way in which a word is made to sound when spoken.
- The way in which the words of a language are made to sound when speaking.
- The act of pronouncing or uttering something.