The most common and most likely answer to this crossword clue is the 12 letter word SELF-RESPECT
I've seen this crossword clue in The Guardian
S
E
L
F
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R
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S
P
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T
More clues leading to the result SELF-RESPECT
Buddy explains!

The straight part
We know that "character among those dignified" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case character among those dignified = self-respect.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 SELF-RESPECT mean?
SELF-RESPECT noun- The knowledge of one's own worth, valuing one's self; pride.