State’s job not finished with excessive enthusiasm (8)
I believe the answer is:
tasmania
'state's' is the definition.
(Tasmania is an example)
'job not finished with excessive enthusiasm' is the wordplay.
'job' becomes 'task' (synonyms).
'not finished' means to remove the last letter.
'with' says to put letters next to each other.
'excessive enthusiasm' becomes 'mania' (I've seen this before).
'task' with its last letter removed is 'tas'.
'tas'+'mania'='TASMANIA'
(Other definitions for tasmania that I've seen before include "Aussie island state" , "Australian island to south of Bass Strait" , "Van Diemen's Land" , "Pacific island" , "Commonwealth state" .)