Heart monitor's first indicator (6)
I believe the answer is:
marrow
'heart' is the definition.
('marrow' can be a synonym of 'heart')
'monitor's first indicator' is the wordplay.
'first' suggests taking the first letters.
'indicator' becomes 'arrow' (I've seen this before).
The first letter of 'monitors' is 'm'.
'm'+'arrow'='MARROW'
(Other definitions for marrow that I've seen before include "The best part" , "Bone filler" , "Edible gourd" , "Vegetable - content of a bone" , "Fatty stuff in bones or large fruit" .)