Fashionable race includes dog who's shy (9)
I believe the answer is:
introvert
'shy' is the definition.
(thesaurus)
'fashionable race includes dog' is the wordplay.
'fashionable' becomes 'in' (in can mean fashionable or trendy).
'race' becomes 'tt'.
'includes' is an insertion indicator.
'dog' becomes 'rover' (Rover is a common name for a pet dog).
'tt' enclosing 'rover' is 'trovert'.
'in'+'trovert'='INTROVERT'
'who's' is the link.
(Other definitions for introvert that I've seen before include "eschewing external contact" , "Withdrawn type" , "Turn inwards" , "Shy type" , "One who's withdrawn" .)