The most common and most likely answer to this crossword clue is the 5 letter word KYRIE
I've seen this crossword clue in The Guardian
K
Y
R
I
E
More clues leading to the result KYRIE
Buddy explains!

The straight part
We know that "Requiem Mass, partly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case requiem mass, partly = kyrie.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 KYRIE mean?
KYRIE noun- A short prayer or petition including the phrase kyrie eleison, meaning “Lord, have mercy”.
- A setting of the traditional kyrie text to music for a Mass.