The most common and most likely answer to this crossword clue is the 9 letter word ELOCUTION
I've seen this crossword clue in The Daily Telegraph
E
L
O
C
U
T
I
O
N
More clues leading to the result ELOCUTION
- Old Conservative involved in clean-up act demonstrates skill in speech
- Shocking treatment, but not ECT? Right, in a manner of speaking
- You must polish, not oil, cue… it’s what Higgins taught
- Delivery of European spot
- Reduction in planning of one oil delivery
- Bad clue, nothing inside to hold setter's name and delivery
Buddy explains!

The straight part
We know that "delivery" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case delivery = elocution.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 ELOCUTION mean?
ELOCUTION noun- The art of public speaking with expert control of gesture and voice, etc.