A rule that breaks the heart of singers (5)
I believe the answer is:
reign
'a rule' is the definition.
(I know that reign is a type of rule)
'breaks the heart of singers' is the wordplay.
'breaks' indicates anagramming the letters.
'the heart of' indicates the central letters.
The central letters of 'singers' are 'inger'.
'inger' with letters rearranged gives 'REIGN'.
'that' acts as a link.
(Other definitions for reign that I've seen before include "Time on throne" , "Monarch's time in the job" , "are unbeatable!" , "Sovereignty" , "Monarch's rule" .)