The most common and most likely answer to this crossword clue is the 11 letter word PERIPATETIC
I've seen this crossword clue in The Times
P
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More clues leading to the result PERIPATETIC
- Precipitate moving or travelling
- Itinerant agent returning, one sad to abandon husband
- Wandering from pier, awfully sad, missing hotel
- Travelling salesman’s back before one, sorry with no hotel
- Wandering fairy’s wretched without husband
- Precipitate action for itinerant
- Wandering through Italy, sorry, not hot
- Ripe bananas — touching, but not hard for moving around
- Vagabond’s precipitate movement
Buddy explains!

The straight part
We know that "travelling" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case travelling = peripatetic.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 PERIPATETIC mean?
PERIPATETIC noun- One who walks about; a pedestrian; an itinerant.
- (usually capitalized) One who accepts the philosophy of Aristotle or his school; an Aristotelian.
- Tending to walk about.
- Constantly travelling; itinerant; nomadic.
- (usually capitalized) Having to do with Aristotle, his philosophy, or the school of thought which he founded -- from the practice of conducting philosophical conversations while taking a walk.