The most common and most likely answer to this crossword clue is the 12 letter word UNFLATTERING
I've seen this crossword clue in The Daily Telegraph
U
N
F
L
A
T
T
E
R
I
N
G
Buddy explains!

The straight part
We know that "not complimentary" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case not complimentary = unflattering.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.
Crossword Answer definitions
UNFLATTERING verb- To show in a bad light; to portray unfavorably.
- Not flattering.