The most common and most likely answer to this crossword clue is the 5 letter word DROVE
I've seen this crossword clue in Independent
D
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More clues leading to the result DROVE
- Army doctor has done with cut
- Forced peace-lover to accept war ultimately
- Peace campaigner having crossed river, acted aschauffeur
- Peace advocate captivates Republican horde
- One able to fly across river avoided public transport?
- Some cattle rustler finally wearing symbol of peace
- Forced rebel leader to be accepted by peacemaker
- Resistance stops bird moving herd
- Crowd drifted back to front
- Host in NY took the plunge welcoming first in reception
Buddy explains!

The straight part
We know that "moving herd" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case moving herd = drove.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 DROVE mean?
DROVE noun- A number of cattle driven to market or new pastures.
- (usually in the plural) A large number of people on the move (literally or figuratively).
- (collective) A group of hares.
- A road or track along which cattle are habitually driven.
- A narrow drain or channel used in the irrigation of land.
- A broad chisel used to bring stone to a nearly smooth surface.
- The grooved surface of stone finished by the drove chisel.
- To provide an impetus for motion or other physical change, to move an object by means of the provision of force thereto.
- To provide an impetus for a non-physical change, especially a change in one's state of mind.
- To displace either physically or non-physically, through the application of force.
- To cause intrinsic motivation through the application or demonstration of force: to impel or urge onward thusly, to compel to move on, to coerce, intimidate or threaten.
- (especially of animals) To impel or urge onward by force; to push forward; to compel to move on.
- To direct a vehicle powered by a horse, ox or similar animal.
- To cause animals to flee out of.
- To move (something) by hitting it with great force.
- To cause (a mechanism) to operate.
- To operate (a wheeled motorized vehicle).
- To motivate; to provide an incentive for.
- To compel (to do something).
- To cause to become.
- To hit the ball with a drive.
- To travel by operating a wheeled motorized vehicle.
- To convey (a person, etc) in a wheeled motorized vehicle.
- To move forcefully.
- To be moved or propelled forcefully (especially of a ship).
- To urge, press, or bring to a point or state.
- To carry or to keep in motion; to conduct; to prosecute.
- To clear, by forcing away what is contained.
- To dig horizontally; to cut a horizontal gallery or tunnel.
- To put together a drive (n.): to string together offensive plays and advance the ball down the field.
- To distrain for rent.
- To separate the lighter (feathers or down) from the heavier, by exposing them to a current of air.
- To be the dominant party in a sex act.
- To herd cattle; particularly over a long distance.
- To finish (stone) with a drove chisel.