The most common and most likely answer to this crossword clue is the 8 letter word DRAWLING
I've seen this crossword clue in Financial Times
D
R
A
W
L
I
N
G
Buddy explains!
The straight part
We know that "Speaking slowly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case speaking slowly = drawling.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 DRAWLING mean?
DRAWLING verb- To drag on slowly and heavily; to while or dawdle away time indolently.
- To utter or pronounce in a dull, spiritless tone, as if by dragging out the utterance.
- To move slowly and heavily; move in a dull, slow, lazy manner.
- To speak with a slow, spiritless utterance, from affectation, laziness, or lack of interest.
- The act of speaking with a drawl.