The most common and most likely answer to this crossword clue is the 6 letter word EDGING
I've seen this crossword clue in The Times
E
D
G
I
N
G
More clues leading to the result EDGING
- Cockney building boundary round field, moving slowly?
- Journalist’s going to reject nothing to reach border
- Moving towards border
- Neatening piece of frayed gingham?
- Ecstasy used by director-general in government fringe
- Dismal sight in cricket – Sri Lankan openers departing, nicking behind
- Opener's dismissed when blocking, getting a nick
- DIG somehow enters England by crawling
- Marching editor has drink with girl
- Being non-committal, leader leaves frame
Buddy explains!

The straight part
We know that "moving slowly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case moving slowly = edging.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 EDGING mean?
EDGING verb- To move an object slowly and carefully in a particular direction.
- To move slowly and carefully in a particular direction.
- (usually in the form 'just edge') To win by a small margin.
- To hit the ball with an edge of the bat, causing a fine deflection.
- To trim the margin of a lawn where the grass meets the sidewalk, usually with an electric or gas-powered lawn edger.
- To furnish with an edge; to construct an edging.
- To furnish with an edge, as a tool or weapon; to sharpen.
- To make sharp or keen; to incite; to exasperate; to goad; to urge or egg on.
- To delay one's orgasm so as to remain almost at the point of orgasm.
- Something that forms, defines or marks the edge.
- Technique involving the placement of the edge of the climbing shoe on a sharp hold.
- The operation of shaping or dressing the edge of anything, as of a piece of metal.
- The sexual technique of maintaining a high level of sexual arousal for an extended period of time without reaching orgasm.