The most common and most likely answer to this crossword clue is the 10 letter word NUMBSKULLS
N
U
M
B
S
K
U
L
L
S
Buddy explains!

The straight part
We know that "nincompoops" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case nincompoops = numbskulls.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 NUMBSKULLS mean?
NUMBSKULLS noun- A dunce, mentally dull or stupid person.
- A person who refuses to learn or grow mentally.
- A traditional name for a fool who serves as the butt of jokes about stupidity.