The most common and most likely answer to this crossword clue is the 7 letter word REQUIEM
I've seen this crossword clue in The Times
R
E
Q
U
I
E
M
More clues leading to the result REQUIEM
- Soldiers composed unfinished Mass, one for the departed
- Wish to avoid second Republican mass for another one
- Mass still mostly interrupting sleep, sort of
- Service concerning peace, short mass
- Insist upon right to leave mass for memorial service
- Rock group, Queen that is, penned elegy
- Need, having forfeited right to get married, some solemn music
- R.E.M. covers mostly soft, sad piece of music
Buddy explains!

The straight part
We know that "another one" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case another one = requiem.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 REQUIEM mean?
REQUIEM noun- A mass (especially Catholic) to honor and remember a dead person.
- A musical composition for such a mass.
- A piece of music composed to honor a dead person.
- Rest; peace
- A large or dangerous shark, specifically, a member of the family Carcharhinidae.