The most common and most likely answer to this crossword clue is the 6 letter word JUSTLY
I've seen this crossword clue in The Guardian
J
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More clues leading to the result JUSTLY
Buddy explains!

The straight part
We know that "In a way that’s fair" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case in a way that’s fair = justly.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 JUSTLY mean?
JUSTLY adverb- In a just or fair manner; rightfully.
- With a just or fair use of language; with good reason, properly.
- With great precision; accurately, exactly.