The most common and most likely answer to this crossword clue is the 2 plus 3 plus 3 plus 5 letter word TO SAY THE LEAST
I've seen this crossword clue in The Times
T
O
S
A
Y
T
H
E
L
E
A
S
T
More clues leading to the result TO SAY THE LEAST
Buddy explains!

The straight part
We know that "not to exaggerate" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case not to exaggerate = to say the least.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.