The most common and most likely answer to this crossword clue is the 9 letter word PEA-BRAIN
I've seen this crossword clue in The Guardian
P
E
A
-
B
R
A
I
N
Buddy explains!

The straight part
We know that "Nana" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case nana = pea-brain.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 PEA-BRAIN mean?
PEA-BRAIN noun- A stupid or clumsy person; a cretin.
- Stupid, clumsy, idiot