Bow is abrupt, say, without heart (6)
I believe the answer is:
curtsy
'bow' is the definition.
(I know that curtsy is a more specific form of the action bow)
'abrupt say without heart' is the wordplay.
'abrupt' becomes 'curt' (I've seen this in another clue).
'without heart' suggests removing the centre.
'say' with its centre removed is 'sy'.
'curt'+'sy'='CURTSY'
'is' is the link.
(Other definitions for curtsy that I've seen before include "Female obeisance bending the knees" , "Bend the knee in respect" , "Kind of respectful bob made by women" , "Bend the knees in a gesture of respect" , "Gesture of respect by women" .)