The most common and most likely answer to this crossword clue is the 9 letter word TRAIPSING
I've seen this crossword clue in Independent
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Buddy explains!

The straight part
We know that "tediously walking around" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case tediously walking around = traipsing.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 TRAIPSING mean?
TRAIPSING verb- To walk in a messy or unattractively casual way; to trail through dirt.
- To walk about, especially when expending much effort, or unnecessary effort.
- To walk (a distance or journey) wearily or with effort; to walk about or over (a place).
- Laborious walking.