The most common and most likely answer to this crossword clue is the 4 letter word GEED
G
E
E
D
Buddy explains!
The straight part
We know that "Moved on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case moved on = geed.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 GEED mean?
GEED verb- Of a horse, pack animal, etc.: to move forward; go faster; or turn in a direction away from the driver, typically to the right.
- To cause an animal to move in this way.
- To agree; to harmonize.
- To suit or fit