The most common and most likely answer to this crossword clue is the 11 letter word CHAIN-SMOKE
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Buddy explains!

The straight part
We know that "Keep dragging" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case keep dragging = chain-smoke.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 CHAIN-SMOKE mean?
CHAIN-SMOKE verb- To smoke cigarettes by continuously lighting one from the glowing end of the previous one.
- To smoke tobacco cigarettes frequently.
- To smoke by continuously lighting one from another.