Endless, unceasing, awful pest (8)
I believe the answer is:
nuisance
'pest' is the definition.
(both can mean an annoying person)
'endless unceasing awful' is the wordplay.
'endless' means to remove the last letter.
'awful' indicates anagramming the letters.
'unceasing' with its final letter taken off is 'unceasin'.
'unceasin' anagrammed gives 'NUISANCE'.
(Other definitions for nuisance that I've seen before include "Annoying thing/person" , "It causes inconvenience or annoyance" , "One causing annoyance" , "Irritant or botheration" , "Bothersome annoying person" .)