The most common and most likely answer to this crossword clue is the 10 letter word CUTTLEFISH
I've seen this crossword clue in Financial Times
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More clues leading to the result CUTTLEFISH
Buddy explains!
The straight part
We know that "user of black ink" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case user of black ink = cuttlefish.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 CUTTLEFISH mean?
CUTTLEFISH noun- Any of various squid-like cephalopods (marine mollusks) of the order Sepiida that have eight arms, two retractable tentacles, and a calcareous internal shell, and can eject a dark ink when threatened