The most common and most likely answer to this crossword clue is the 9 letter word STARCHIER
I've seen this crossword clue in The Times
S
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More clues leading to the result STARCHIER
Buddy explains!

The straight part
We know that "more stiff" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case more stiff = starchier.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 STARCHIER mean?
STARCHIER adjective- Of or pertaining to starch.
- Containing starch.
- Having the quality of fabric starch as applied to fabric; stiff, hard; starched.
- Having a starched personality; stiffly formal.