Gave Hogarth lip about the print (10)
I believe the answer is:
lithograph
'the print' is the definition.
(lithograph is a kind of print)
'gave hogarth lip' is the wordplay.
'gave' indicates an anagram (I've seen 'giving' mean this (the letters give the letters for another word)).
'hogarth'+'lip'='hogarthlip'
'hogarthlip' anagrammed gives 'LITHOGRAPH'.
'about' acts as a link.
(Other definitions for lithograph that I've seen before include "illustration" , "Type of print" .)