Story books given to public library, initially (4)
I believe the answer is:
plot
'story' is the definition.
(I know that plot is a type of story)
'books given to public library initially' is the wordplay.
'books' becomes 'OT' (Old Testament).
'given to' says to put letters next to each other.
'initially' suggests taking the first letters.
The first letters of 'public library' is 'pl'.
'ot' put after 'pl' is 'PLOT'.
(Other definitions for plot that I've seen before include "Scheme; graph" , "Storyline or piece of land" , "Design" , "Story or piece of land" , "Mark position" .)