Fish eaten by Martha Kearney (4)
I believe the answer is:
hake
'fish' is the definition.
(type of fish)
'eaten by martha kearney' is the wordplay.
'eaten by' indicates the answer is hidden within the clue.
'HAKE' is hidden within 'martha kearney'.
(Other definitions for hake that I've seen before include "Common food fish" , "Food fish related to the cod" , "Swimmer" , "Food fish; rhymes with create" , "Cod-like fish" .)