The most common and most likely answer to this crossword clue is the 9 letter word PERCOLATE
I've seen this crossword clue in Independent
P
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The straight part
We know that "filter" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case filter = percolate.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 PERCOLATE mean?
PERCOLATE noun- A liquid that has been percolated.
- To pass a liquid through a porous substance; to filter.
- To drain or seep through a porous substance.
- To make (coffee) in a percolator.
- To spread slowly or gradually; to slowly become noticed or realised.