The most common and most likely answer to this crossword clue is the 7 letter word SANDFLY
I've seen this crossword clue in The Times
S
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More clues leading to the result SANDFLY
Buddy explains!

The straight part
We know that "bloodsucker" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case bloodsucker = sandfly.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 SANDFLY mean?
SANDFLY noun- Any of various small flies of the genera Lutzomyia and Phlebotomus whose females suck the blood of vertebrates and thus spread leishmaniasis.
- A small fly of the genus Austrosimulium.
- A biting midge (family Ceratopogonidae).