The most common and most likely answer to this crossword clue is the 11 letter word TEENY-WEENY
I've seen this crossword clue in The Times
T
E
E
N
Y
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W
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Y
More clues leading to the result TEENY-WEENY
Buddy explains!

The straight part
We know that "Very little" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case very little = teeny-weeny.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 TEENY-WEENY mean?
TEENY-WEENY adjective- Very small; tiny; minuscule.