The most common and most likely answer to this crossword clue is the 9 letter word DERMATOME
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The straight part
We know that "that gets under the skin" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that gets under the skin = dermatome.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 DERMATOME mean?
DERMATOME noun- An instrument used surgically to remove a thin slice of skin for grafting
- An area of skin which is innervated by afferent nerve fibers coming to a single posterior spinal root. Compare: myotome.
- The cutis plate.