Groan about painting outside that's self-important (8)
I believe the answer is:
arrogant
'self-important' is the definition.
(synonyms)
'groan about painting outside' is the wordplay.
'about' indicates an anagram.
'painting' becomes 'art' (painting is an art).
'outside' means one lot of letters goes inside another (some letters go outside others).
'groan' is an anagram of 'rogan'.
'rogan' going into 'art' is 'ARROGANT'.
'that's' is the link.
(Other definitions for arrogant that I've seen before include "Overweening" , "Cocky" , "Showing an offensive sense of superiority" , "High and mighty" , "Having an exaggerated sense of one's own importance" .)