In love, shown by distracted demeanour (9)
I believe the answer is:
enamoured
'in love' is the definition.
(I've seen this before)
'distracted demeanour' is the wordplay.
'distracted' indicates anagramming the letters.
'demeanour' with letters rearranged gives 'ENAMOURED'.
'shown by' is the link.
(Other definitions for enamoured that I've seen before include "Inspired with love" , "Very fond of" , "Smitten" , "Besotted" , "Filled with love" .)