This artist does a lot of eating out (6)
I believe the answer is:
etcher
'this artist' is the definition.
(etcher is a kind of artist)
'a lot of eating out' is the wordplay.
'a lot' becomes 'c'.
'of eating' becomes 'ether' (I can't justify this - if you can you should believe this answer much more).
'out' indicates putting letters inside.
'c' placed inside 'ether' is 'ETCHER'.
'does' is the link.
Can you help me to learn more?
(Other definitions for etcher that I've seen before include "Artist using acid on metal" , "Engraver" , "One making an impression" , "A designing individual" , "One sharply scores" .)