Tattoos damaged skin (4)
I believe the answer is:
inks
'tattoos' is the definition.
'damaged skin' is the wordplay.
'damaged' is an anagram indicator.
'skin' is an anagram of 'INKS'.
(Other definitions for inks that I've seen before include "Sink beneath writing fluids" , "Printers' mediums" , "Printing fluids" , "Printers' media" , "Liquids used for printing" .)