The most common and most likely answer to this crossword clue is the 9 letter word NONSMOKER
I've seen this crossword clue in The Times
N
O
N
S
M
O
K
E
R
More clues leading to the result NONSMOKER
Buddy explains!

The straight part
We know that "One hates dragging" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one hates dragging = nonsmoker.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 NONSMOKER mean?
NONSMOKER noun- Somebody who does not smoke tobacco.
- A railway carriage where smoking tobacco is not permitted.