The most common and most likely answer to this crossword clue is the 4 letter word PLOD
I've seen this crossword clue in The Times
P
L
O
D
More clues leading to the result PLOD
Buddy explains!

The straight part
We know that "Copper" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case copper = plod.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 PLOD mean?
PLOD noun- A slow or labored walk or other motion or activity.
- To walk or move slowly and heavily or laboriously (+ on, through, over).
- To trudge over or through.
- To toil; to drudge; especially, to study laboriously and patiently.
- A puddle.
- (mildly, usually with "the") the police, police officers
- (mildly) a police officer, especially a low-ranking one.