Sign a rough tap damaged (9)
I believe the answer is:
autograph
'sign' is the definition.
(autographing is a kind of signing)
'a rough tap damaged' is the wordplay.
'damaged' is an anagram indicator.
'rough'+'tap'='roughtap'
'roughtap' anagrammed gives 'utograph'.
'a'+'utograph'='AUTOGRAPH'
(Other definitions for autograph that I've seen before include "Signer will give this" , "(Celebrity's) signature" , "One's signature" , "a collector's item perhaps" , "(Celebrity) signature" .)