Fashionable writer to sign book (8)
I believe the answer is:
inscribe
'sign book' is the definition.
'inscribe' can be an answer for 'book' (thesaurus). I'm not certain of the 'sign' bit.
'fashionable writer' is the wordplay.
'fashionable' becomes 'in' (in can mean fashionable or trendy).
'writer' becomes 'scribe' (scribe is a kind of writer).
'in'+'scribe'='INSCRIBE'
'to' acts as a link.
Can you help me to learn more?
(Other definitions for inscribe that I've seen before include "Engrave; enter (name in list)" , "Put dedication into" , "Write upon, formally perhaps" , "chase" , "Write; etch" .)