The most common and most likely answer to this crossword clue is the 12 letter word OVEREXPOSURE
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result OVEREXPOSURE
Buddy explains!
The straight part
We know that "Excess publicity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case excess publicity = overexposure.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 OVEREXPOSURE mean?
OVEREXPOSURE noun- Excessive exposure.
- Of a famous person, excessive publicity, publication or reporting regarding that person.
- Exposure of film to light during the development process for a longer time than is required to accurately produce the image.