The most common and most likely answer to this crossword clue is the 3 plus 3 letter word ALL BUT
I've seen this crossword clue in The Times
A
L
L
B
U
T
More clues leading to the result ALL BUT
- Just about to vacate local when neighbour’s come round
- Neighbour swallows Liberal line pretty much
- Very nearly join, after intervention of Lord Lieutenant
- Liberals kept in touch, just about
- Practically everyone, contrary to expectation
- Almost everything’s built without it in France
- Very nearly the whole amount, contrary to expectation
- Nearly a couple of litres in a cask
Buddy explains!

The straight part
We know that "Very nearly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case very nearly = all but.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.