The most common and most likely answer to this crossword clue is the 9 letter word LIMELIGHT
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result LIMELIGHT
- Easily moved about male priest, the focus of attention
- Fruit fair’s conspicuous position
- Writer’s Spanish article pricks faint public interest
- Maiden in story, delicate in glare of publicity
- Travelling mile over land, celebrities long for it
- Story about motorway illumination becomes focus of attention
- Easily moved about male priest getting media attention
- Fruit easy to transport that’s sought by celebrity
- Fib about male getting insubstantial public exposure?
- Story about male accompanied by frivolous sort of publicity
Buddy explains!

The straight part
We know that "media attention" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case media attention = limelight.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 LIMELIGHT mean?
LIMELIGHT noun- A type of stage lighting once used in theatres and music halls, producing a bright light by the use of incandescent quicklime.
- (by extension) Attention, notice, a starring or central role, present fame.
- To illuminate with limelight