Quite right — heart is fluttering (6)
I believe the answer is:
rather
'quite' is the definition.
(synonyms)
'right heart is fluttering' is the wordplay.
'right' becomes 'R' (common abbreviation).
'is fluttering' indicates anagramming the letters.
'heart' anagrammed gives 'ather'.
'r'+'ather'='RATHER'
(Other definitions for rather that I've seen before include "Slightly, more so than not (6" , "A bit" , "On the contrary or to some extent" , "Most certainly" , "More willingly, by preference" .)