Nietzsche lacks zest at recess (5)
I believe the answer is:
niche
'recess' is the definition.
(I know that recess can be written as niche)
'nietzsche lacks zest' is the wordplay.
'lacks' suggests deleting specific letters.
'nietzsche' with 'zest' removed is 'NICHE'.
'at' acts as a link.
(Other definitions for niche that I've seen before include "Position well suited to the occupier" , "Specialized market" , "Suitable spot" , "good spot!" , "Recess - alcove" .)