The most common and most likely answer to this crossword clue is the 8 letter word ANTIPHON
I've seen this crossword clue in The Times
A
N
T
I
P
H
O
N
More clues leading to the result ANTIPHON
- One of Mitford’s aristos accepting suggestion for psalm
- One of Mitford’s aristos accepting idea for psalm?
- Dump Beethoven's Fifth amid unknown music
- An extra payment given to husband performing church music
- Presumably favouring genuine short hymn
- Against mobile being cut off in part of sung service
- Man outside one boozer provides church music
- One Direction not hip playing church music
- One gentle introduction to heaven in Bruckner’s church music
Buddy explains!

The straight part
We know that "part of sung service" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of sung service = antiphon.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 ANTIPHON mean?
ANTIPHON noun- A devotional piece of music sung responsively.
- A response or reply.