The most common and most likely answer to this crossword clue is the 4 letter word SCAR
I've seen this crossword clue in The Daily Telegraph
S
C
A
R
More clues leading to the result SCAR
- Mark left by injury in steep rocky outcrop
- Damage statuette with no head
- Evidence of injury and endless panic
- Mark film award, overlooking nothing
- Mark close to bedside put off alarm
- Small vehicle making permanent mark
- Small vehicle showing damage
- Mark for good spelling, chemistry and reading: first in each
- Crazy Ottoman leaving large island for cliff
- Mark Rothko’s first piece after unfinished study
Buddy explains!

The straight part
We know that "Damage" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case damage = scar.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 SCAR mean?
SCAR noun- A permanent mark on the skin, sometimes caused by the healing of a wound.
- (by extension) A permanent negative effect on someone's mind, caused by a traumatic experience.
- Any permanent mark resulting from damage.
- To mark the skin permanently.
- To form a scar.
- To affect deeply in a traumatic manner.
- A cliff or rock outcrop.
- A rock in the sea breaking out from the surface of the water.
- A bare rocky place on the side of a hill or mountain.
- A marine food fish, the scarus or parrotfish (family Scaridae).