Character having sloth arising, when around books (4)
I believe the answer is:
iota
'character' is the definition.
(iota is a kind of character)
'sloth arising when around books' is the wordplay.
'sloth' becomes 'ai' (ai is a kind of sloth).
'arising' is a reversal indicator.
'when around' is an insertion indicator.
'books' becomes 'ot' (Old Testament).
'ai' back-to-front is 'ia'.
'ia' placed around 'ot' is 'IOTA'.
'having' is the link.
(Other definitions for iota that I've seen before include "Smidgen" , "Smidgeon" , "Jot, particle" , "Old letter" , "Foreign character" .)