Attracted by quirky demeanour (9)
I believe the answer is:
enamoured
'attracted' is the definition.
(enamouring is a kind of attracting)
'quirky demeanour' is the wordplay.
'quirky' indicates anagramming the letters.
'demeanour' is an anagram of 'ENAMOURED'.
'by' is the link.
(Other definitions for enamoured that I've seen before include "Filled with love" , "Greatly taken with" , "Besotted" , "In love with - named rou (anag)" , "Bewitched" .)