Cryptic crossword clue
Mad Hatter’s rig is more respectable 10

The most common and most likely answer to this crossword clue is the 10 letter word STRAIGHTER

I've seen this crossword clue in The Guardian
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Buddy explains!

The straight part
We know that "more respectable" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case more respectable = straighter.
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 STRAIGHTER mean?

STRAIGHTER adjective
  1. Not crooked or bent; having a constant direction throughout its length.
  2. (of a path, trajectory, etc.) Direct, undeviating.
  3. Perfectly horizontal or vertical; not diagonal or oblique.
  4. Describing the bat as held so as not to incline to either side; on, or near a line running between the two wickets.
  5. Direct in communication; unevasive, straightforward.
  6. Free from dishonesty; honest, law-abiding.
  7. Serious rather than comedic.
  8. In proper order; as it should be.
  9. In a row, in unbroken sequence; consecutive.
  10. Describing the sets in a match of which the winner did not lose a single set.
  11. Making no exceptions or deviations in one's support of the organization and candidates of a political party.
  12. Containing the names of all the regularly nominated candidates of a party and no others.
  13. Conventional, mainstream, socially acceptable.
  14. Heterosexual, attracted to people of the opposite sex.
  15. (of a romantic or sexual relation) Occurring between people of opposite sex.
  16. Not using alcohol, drugs, etc.
  17. Not plus size; thin.
  18. Strait; narrow.
  19. Stretched out; fully extended.
  20. Thorough; utter; unqualified.
  21. Of spirits: undiluted, unmixed; neat.
  22. Concerning the property allowing the parallel-transport of vectors along a course that keeps tangent vectors remain tangent vectors throughout that course (a course which is straight, a straight curve, is a geodesic).
STRAIGHTER noun
  1. A cigarette, particularly one containing tobacco instead of marijuana. Also straight.

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