Race to supply lasting literary work (7)
I believe the answer is:
classic
This clue is a double definition.
'race' is the first definition.
(I've seen this before)
'lasting literary work' is the second definition.
(I've seen this before)
'to supply' is the link.
(Other definitions for classic that I've seen before include "Artistic work of the highest excellence" , "Model" , "work of the highest quality" , "Timeless-quality work; a race" , "Work of established excellence (7)" .)