The most common and most likely answer to this crossword clue is the 12 letter word UNDERCURRENT
I've seen this crossword clue in The Times
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More clues leading to the result UNDERCURRENT
Buddy explains!
The straight part
We know that "influence that’s hidden" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case influence that’s hidden = undercurrent.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 UNDERCURRENT mean?
UNDERCURRENT noun- A current of water which flows under the surface, and often in a different direction from surface currents.
- A tendency of feeling or opinion that is concealed rather than exposed.
- To flow under some surface.