Kind of chop academician fed to a shrew? (6)
I believe the answer is:
karate
'kind of chop' is the definition.
(I've seen this in another clue)
'academician fed to a shrew?' is the wordplay.
'academician' becomes 'RA' (member of the Royal Academy of Arts).
'fed to' is an insertion indicator.
'a shrew?' becomes 'kate' (Katherina or Kate in The Taming of the Shrew).
'ra' going into 'kate' is 'KARATE'.
(Other definitions for karate that I've seen before include "Japanese martial art" , "A Jap. martial art" , "method of fighting" , "Jap. combat; sort of chop" , "Unarmed-combat system" .)