Dead to the world as zest's on the rise (6)
I believe the answer is:
asleep
'dead to the world' is the definition.
(I've seen this before)
'as zest's on the rise' is the wordplay.
'zest' becomes 'peel' (I've seen this in another clue).
'on the rise' says the letters should be written in reverse (in a down clue, letters go up).
'peel' reversed gives 'leep'.
'as'+'leep'='ASLEEP'
(Other definitions for asleep that I've seen before include "Please (anag) - numb" , "Please be at rest (6)." , "this fast?" , "Napping" , "Dormant; inattentive" .)