Horrid girl starts cheap book (5,8)
I believe the answer is:
penny dreadful
'cheap book' is the definition.
(I've seen this before)
'horrid girl starts' is the wordplay.
'horrid' becomes 'dreadful'.
'girl' becomes 'penny' (woman's name).
'starts' says to put letters next to each other.
'dreadful' after 'penny' is 'PENNY-DREADFUL'.
(Other definitions for penny dreadful that I've seen before include "Cheap, sensational novel" , "Cheap pulp novel" , "Junior relation of the shilling shocker?" , "worthless novel" , "Old publication" .)