Island taking back letters from Peter Cook (5)
I believe the answer is:
crete
'island' is the definition.
(Greek island)
'back letters from peter cook' is the wordplay.
'back' says the letters should be written in reverse.
'letters from' says the answer is hidden in the clue (a selection of letters from the clue).
'eterc' is hidden in the letters of 'peter cook'.
'eterc' backwards is 'CRETE'.
'taking' acts as a link.
(Other definitions for crete that I've seen before include "Herakleion its big port" , "Greek island, capital Heraklion" , "Island whose largest city is Heraklion" , "Island Germans took, 1941" , "Large Mediterranean island" .)