Flutter with a pulse (4)
I believe the answer is:
beat
'pulse' is the definition.
('beat' can be a synonym of 'pulse')
'flutter with a' is the wordplay.
'flutter' becomes 'bet' (I've seen this in other clues).
'with' is an insertion indicator.
'bet' enclosing 'a' is 'BEAT'.
(Other definitions for beat that I've seen before include "Strike; stir vigorously" , "Strike repeatedly" , "Come out better than in a competition" , "patrol route?" , "course run regularly" .)