The most common and most likely answer to this crossword clue is the 8 letter word PONYTAIL
I've seen this crossword clue in Financial Times
P
O
N
Y
T
A
I
L
More clues leading to the result PONYTAIL
- Hairstyle associated with Exmoor, perhaps? It depends
- Tiny opal possibly worn behind the ears
- Hairstyle that could have distracted any pilot?
- £25 tip that could go to one’s head
- Hairstyle offering £25 back?
- Bucket full of poor Tony’s hair?
- Hairstyle 25 pounds — join queue
- Hair arrangement reworked into play
- Put £25 on dog in Barnet
- Alternative to a bun is assortment of pita only
Buddy explains!

The straight part
We know that "Barnet" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case barnet = ponytail.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 PONYTAIL mean?
PONYTAIL noun- A hairstyle where the hair is pulled back and tied into a single "tail" which hangs down behind the head.