The most common and most likely answer to this crossword clue is the 9 letter word FIVE-STAR
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More clues leading to the result FIVE-STAR
Buddy explains!

The straight part
We know that "First class" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case first class = five-star.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 FIVE-STAR mean?
FIVE-STAR adjective- The best quality
- A hard slap on bare skin with a hand that leaves a red, fully hand-shaped mark.
- A mark from such a slap.
- To slap someone hard with the hand on bare skin, leaving a red, fully hand-shaped mark.