The most common and most likely answer to this crossword clue is the 7 letter word ALLERGY
I've seen this crossword clue in The Guardian
A
L
L
E
R
G
Y
More clues leading to the result ALLERGY
- Partner touring work unit gets bad reaction
- Good to move down exhibition hall showing sensitivity
- Hypersensitivity of friend without some measure of work
- Every sort of grey sensitivity
- Art museum delaying its opening provokes an abnormal reaction
- Funny reaction, as gods start moving in right direction
- Funny reaction in left ear, when raving about Fifty Shades of Grey?
- Cause of reaction that’s largely violent
- Person’s bad reaction largely misplaced
- Cause of ill feeling disrupting gallery
Buddy explains!

The straight part
We know that "sensitivity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sensitivity = allergy.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 ALLERGY mean?
ALLERGY noun- A disorder of the immune system causing adverse reactions to substances (allergens) not harmful to most and marked by the body's production of histamines and associated with atopy, anaphylaxis, and asthma.
- Any condition of hypersensitivity to a substance.
- Altered susceptibility to a first treatment as exhibited in reaction to a subsequent one.
- An antipathy, as toward a person or activity.