The most common and most likely answer to this crossword clue is the 10 letter word PHLEBOTOMY
I've seen this crossword clue in Financial Times
P
H
L
E
B
O
T
O
M
Y
More clues leading to the result PHLEBOTOMY
Buddy explains!

The straight part
We know that "opening vessel" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case opening vessel = phlebotomy.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 PHLEBOTOMY mean?
PHLEBOTOMY noun- The opening of a vein, either to withdraw blood or for letting blood; venesection.