Beat of romantic's heart, yearning to have matchmaker's introductions (6)
I believe the answer is:
rhythm
'beat' is the definition.
(I know that beat can be written as rhythm)
'romantic's heart yearning to have matchmaker's introductions' is the wordplay.
'introductions' says to take the initial letters (the letters which introduce the word).
The initial letters of 'romantics heart yearning to have matchmakers' is 'RHYTHM'.
'of' acts as a link.
(Other definitions for rhythm that I've seen before include "Regular beat in music" , "A musical essential" , "The basic beat, of a piece of music say" , "Strong regular repeated pattern of sound" , "Regular occurrence of stresses, pulse, etc" .)