Heading for library: repeat, able to read (8)
I believe the answer is:
literate
'able to read' is the definition.
(I've seen this before)
'heading for library repeat' is the wordplay.
'heading for' indicates taking the first letters.
'repeat' becomes 'iterate' ('iterate' can be a synonym of 'repeat').
The first letter of 'library' is 'l'.
'l'+'iterate'='LITERATE'
(Other definitions for literate that I've seen before include "Able to read and write" , "Scholarly" , "well expressed" , "Learned" , "Relate it, being well read" .)