The most common and most likely answer to this crossword clue is the 10 letter word UNDERSTATE
I've seen this crossword clue in The Times
U
N
D
E
R
S
T
A
T
E
Buddy explains!

The straight part
We know that "Make little of" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case make little of = understate.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 UNDERSTATE mean?
UNDERSTATE verb- To state (something) with less completeness than needed; to minimise or downplay.
- To state (something) with a lack of emphasis, in order to express irony.
- To state a quantity that is too low.