Artist went quickly through colour outline of tattoo (10)
I believe the answer is:
tintoretto
'artist' is the definition.
(I've seen this before)
'went quickly through colour outline of tattoo' is the wordplay.
'went quickly' becomes 'tore' (I've seen this in another clue).
'through' is an insertion indicator (inserted letters go through the word).
'colour' becomes 'tint' (tint is a kind of colour).
'outline of' means to remove the middle letters (outline refers to the letters on the edges).
'tattoo' with its middle removed is 'to'.
'tore' put inside 'tint' is 'tintoret'.
'tintoret'+'to'='TINTORETTO'
(Other definitions for tintoretto that I've seen before include "16th century Italian painter" , "Artist" , "Italian painter, d. 1594" .)