Absolutely determined (4,3)
I believe the answer is:
dead set
'absolutely determined' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for dead set that I've seen before include "Absolutely determined, bent on" , "A determined attack - from extinct group?" , "A determined attack, sounds moribund" , "Absolutely - sedated (anag)" , "Fixed in one's purpose" .)