The 'beat' of a giant heart! (3)
I believe the answer is:
tan
'the beat' is the definition.
(tan can mean to beat or hit)
'giant heart' is the wordplay.
'giant' becomes 'titanic' (I've seen this before).
'heart' says to take the centre.
The middle of 'titanic' is 'TAN'.
'of a' is the link.
(Other definitions for tan that I've seen before include "Tawny" , "Yellowish brown" , "Process" , "Go brown" , "Curry" .)