The most common and most likely answer to this crossword clue is the 9 letter word EUPHEMISM
I've seen this crossword clue in Independent
E
U
P
H
E
M
I
S
M
More clues leading to the result EUPHEMISM
- It means sex in this pub — I see mum hustling outside
- One’s left us for dead
- Delicate choice of terminology, possibly making me use Phi, mark
- Polite expression for you being against heartless feminism, we hear
- Mum’s pie – he used a polite term
- Left for dead, for example
- One’s left us for dead?
- Substitute is excited, on edge in volatile semi
- Crumbling empire turning to mush after king kicked the bucket, for instance
- Mum's EP he and I palmed off using polite term
Buddy explains!

The straight part
We know that "Delicate choice of terminology" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case delicate choice of terminology = euphemism.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 EUPHEMISM mean?
EUPHEMISM noun- The use of a word or phrase to replace another with one that is considered less offensive, blunt or vulgar than the word or phrase which it replaces.
- A word or phrase that is used to replace another in this way.