The most common and most likely answer to this crossword clue is the 8 letter word SALIENCE
I've seen this crossword clue in The Daily Telegraph
S
A
L
I
E
N
C
E
Buddy explains!

The straight part
We know that "prominence" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case prominence = salience.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 SALIENCE mean?
SALIENCE noun- The condition of being salient.
- A highlight; perceptual prominence, or likelihood of being noticed.
- Relative importance based on context.