The most common and most likely answer to this crossword clue is the 7 letter word TRUMPED
I've seen this crossword clue in The Daily Telegraph
T
R
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M
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D
More clues leading to the result TRUMPED
Buddy explains!

The straight part
We know that "False" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case false = trumped.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 TRUMPED mean?
TRUMPED verb- To play on (a card of another suit) with a trump.
- To play a trump, or to take a trick with a trump.
- To get the better of, or finesse, a competitor.
- To impose unfairly; to palm off.
- To supersede.
- To outweigh; be stronger, greater, bigger than or in other way superior to.
- To blow a trumpet.
- To flatulate.