It's passion that gives an heiress heart! (3)
I believe the answer is:
ire
'it's passion' is the definition.
(ire is passionate anger)
'an heiress heart' is the wordplay.
'heart' means to look at the middle letters.
The middle letters of 'heiress' are 'IRE'.
'that gives' acts as a link.
(Other definitions for ire that I've seen before include "Annoyance, vexation" , "Hot temper" , "Anger, annoyance" , "Outrage" , "Fury" .)