The most common and most likely answer to this crossword clue is the 1 plus 4 plus 3 letter word O SOLE MIO
I've seen this crossword clue in Financial Times
O
S
O
L
E
M
I
O
More clues leading to the result O SOLE MIO
- Hint of olive oil, some tossed: an Italian standard
- Old, almost stately Italian love song
- Single note in old, old song
- Song starts in Oval Office comprising one note
- Lime’s cooked with duck three times – Neapolitan composition
- I’m back after roaming loose, finding love in the air in Italy
- Neapolitan hit: “I love to finish old unfinished grave”
- Moose oil refined for a song
- This tuned rendering melodious note?
- Song that’s old and almost completely glum, I love!
Buddy explains!

The straight part
We know that "Neapolitan hit" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case neapolitan hit = o sole mio.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.