The most common and most likely answer to this crossword clue is the 7 letter word BUMBOAT
I've seen this crossword clue in The Times
B
U
M
B
O
A
T
Buddy explains!

The straight part
We know that "supply vessel" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case supply vessel = bumboat.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 BUMBOAT mean?
BUMBOAT noun- A small boat used for carrying provisions to ships lying at anchor in a harbour.