The most common and most likely answer to this crossword clue is the 7 letter word ELEGISE
I've seen this crossword clue in The Daily Telegraph
E
L
E
G
I
S
E
Buddy explains!

The straight part
We know that "Be mournful" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case be mournful = elegise.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 ELEGISE mean?
ELEGISE verb- To compose an elegy for.
- To compose an elegy.
- To praise, as if in an elegy.