The most common and most likely answer to this crossword clue is the 9 letter word MOUSTACHE
I've seen this crossword clue in The Times
M
O
U
S
T
A
C
H
E
More clues leading to the result MOUSTACHE
- Hair growth over parting is bound to be longer
- Came south after breaking handlebar?
- Hair growth over parting has to hurt
- Grimace about cold, wearing headgear over whiskers
- Fancy costume with hat briefly worn in November?
- Walrus, typically floppy stomach gathering mud, discovered close to shore
- Witty remark about compilers with long whiskers
- Growth of a man without love has to be uncomfortable?
- Growing row over a speaker
- Have to admit zero pain from growth on lip
Buddy explains!

The straight part
We know that "Hair growth" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hair growth = moustache.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 MOUSTACHE mean?
MOUSTACHE noun- A growth of facial hair between the nose and the upper lip.