The most common and most likely answer to this crossword clue is the 12 letter word PIANIS[S]IMO
P
I
A
N
I
S
[
S
]
I
M
O
Buddy explains!

The straight part
We know that "Very softly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case very softly = pianis[s]imo.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 PIANIS[S]IMO mean?
PIANIS[S]IMO noun- A dynamic sign indicating that a portion of music should be played pianissimo.
- A portion of music that is played very softly.
- To be played very softly.