This last sprite, Hart asserted, based on his own assertion (4-10)
I believe the answer is:
self-proclaimed
'this last sprite hart asserted based on his own assertion' is the definition.
The definition suggests an adjective which matches the answer.
'this last sprite hart asserted' is the wordplay.
'this last sprite hart' becomes 'self' (I can't explain this - if you can you should believe this answer much more).
'asserted' becomes 'proclaimed' (proclaiming is a kind of asserting).
'self'+'proclaimed'='SELF-PROCLAIMED'
Can you help me to learn more?
(Other definitions for self-proclaimed that I've seen before include "Personally announced without others' backing" , "Declared (without others' endorsement)" .)