Hopeful when Private Eye published second of stories (8)
I believe the answer is:
aspirant
'hopeful' is the definition.
(similar in meaning)
'when private eye published second of stories' is the wordplay.
'when' becomes 'as' (eg 'when I walked' means 'as I walked').
'private eye' becomes 'PI' (synonyms).
'published' becomes 'ran' (running is a kind of publishing).
'second of stories' becomes 't' (2nd letter of 'stories').
'as'+'pi'+'ran'+'t'='ASPIRANT'
(Other definitions for aspirant that I've seen before include "One seeking eg promotion" , "Candidate; one with a desire to succeed" , "Partisan (anag)" , "One works hard to achieve something" , "One is working hard to achieve something" .)