Persuade somehow, believing book is missing (8)
I believe the answer is:
inveigle
'persuade' is the definition.
(inveigling is a kind of persuading)
'somehow believing book is missing' is the wordplay.
'somehow' indicates an anagram.
'book' becomes 'b'.
'is missing' is a deletion indicator.
'believing' with 'b' removed is 'elieving'.
'elieving' is an anagram of 'INVEIGLE'.
(Other definitions for inveigle that I've seen before include "Con" , "Lead on, entice" , "Persuade by flattery" , "Persuade by deception" , "Induce by trick, cajole" .)