Aspired to become a literary giant (7)
I believe the answer is:
despair
'a literary giant' is the definition.
(Despair is a giant in The Pilgrim's Progress)
'aspired to become' is the wordplay.
'to become' indicates anagramming the letters.
'aspired' anagrammed gives 'DESPAIR'.
(Other definitions for despair that I've seen before include "Complete absence of hope" , "Total loss of hope" , "Feeling of hopelessness" , "A spider (anag.)" , "The feeling that nothing will turn out well" .)