The most common and most likely answer to this crossword clue is the 9 letter word DISFAVOUR
I've seen this crossword clue in The Times
D
I
S
F
A
V
O
U
R
Buddy explains!

The straight part
We know that "Unpopularity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case unpopularity = disfavour.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 DISFAVOUR mean?
DISFAVOUR noun- Lack of favour; displeasure.
- An unkindness; a disobliging act.
- A state of being out of favour.
- To show lack of favour or antipathy towards.