The most common and most likely answer to this crossword clue is the 9 letter word CAPILLARY
I've seen this crossword clue in The Daily Telegraph
C
A
P
I
L
L
A
R
Y
Buddy explains!

The straight part
We know that "Vessel" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case vessel = capillary.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 CAPILLARY mean?
CAPILLARY noun- A narrow tube.
- Any of the small blood vessels that connect arteries to veins.
- Of or pertaining to hair.
- Pertaining to a narrow tube.
- Of, relating to, or caused by surface tension.