Artist periodically seeing red frames shows anger (8)
I believe the answer is:
irritate
'anger' is the definition.
(thesaurus)
'artist periodically seeing red frames' is the wordplay.
'periodically' indicates alternate letters (letters must be selected 'every so often').
'seeing red' becomes 'irate' (I've seen this in another clue).
'frames' means one lot of letters goes inside another (outside letters frame the inside letters).
The alternating letters of 'artist' are 'rit'.
'rit' going into 'irate' is 'IRRITATE'.
'shows' acts as a link.
(Other definitions for irritate that I've seen before include "Chafe, annoy" , "Rattier, I may be annoying" , "Provoke" , "Wind up" , "Needle" .)