Pay fine for removing cover on books (4)
I believe the answer is:
foot
'pay' is the definition.
(as in footing the bill)
'fine for removing cover on books' is the wordplay.
'fine' becomes 'f' (abbreviation in pencil classifications).
'removing cover' says to take the centre (I've seen 'removing covers' mean this (letters which cover the word are removed)).
'on' says to put letters next to each other.
'books' becomes 'OT' (Old Testament).
The central letter of 'for' is 'o'.
'f'+'o'+'ot'='FOOT'
(Other definitions for foot that I've seen before include "Labour Party leader, 1980-83" , "Measure - part of body" , "Imperial distance" , "Metrical unit; pay (a bill)" , "Distance to the end of a limb?" .)