The most common and most likely answer to this crossword clue is the 10 letter word TRIVIALITY
I've seen this crossword clue in The Times
T
R
I
V
I
A
L
I
T
Y
More clues leading to the result TRIVIALITY
Buddy explains!

The straight part
We know that "a tiny thing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a tiny thing = triviality.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 TRIVIALITY mean?
TRIVIALITY noun- The quality of being trivial or unimportant.
- Something which is trivial or unimportant.