Nuisance admits a lack of energy at school producing reused manuscript (10)
I believe the answer is:
Here is my best explanation:
'manuscript' is the definition.
(palimpsest is a kind of manuscript)
'nuisance admits a lack of energy at school' is the wordplay.
'nuisance' becomes 'pest' (I've seen this before).
'admits' indicates putting letters inside.
'lack of energy at' becomes 'limp' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'school' becomes 's'.
'pest' going around 'alimps' is 'palimpsest'.
'producing reused' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.
(Other definitions for palimpsest that I've seen before include "Simple taps (anag.); a manuscript", "recycled document", "Recycled manuscript" and "Reused parchment".)