More than usually insulting, artist chucked press out (7)
I believe the answer is:
extrude
'press out' is the definition.
(to extrude is to stick out)
'more than usually insulting artist chucked' is the wordplay.
'more than usually' becomes 'extra' (extra can mean to a greater level than normal).
'insulting' becomes 'rude'.
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'chucked' is a deletion indicator.
'extra'+'rude'='extrarude'
'extrarude' with 'ra' removed is 'EXTRUDE'.
(Other definitions for extrude that I've seen before include "Eject" , "Thrust or force out" , "feature obviously?" , "Force out (through die)" , "Stick out" .)