The most common and most likely answer to this crossword clue is the 2 plus 4 letter word TE DEUM
I've seen this crossword clue in The Daily Telegraph
T
E
D
E
U
M
More clues leading to the result TE DEUM
Buddy explains!
The straight part
We know that "that’s sung in church" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that’s sung in church = te deum.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.