Perhaps Elizabeth I’s governess having change of heart (5)
I believe the answer is:
tudor
'perhaps elizabeth i's' is the definition.
(Elizabeth I was a Tudor queen)
I don't understand the rest of the clue.
(Other definitions for tudor that I've seen before include "eg Henry VIII" , "(Pertaining to) royal house" , "Mary" , "English royal dynasty" , "regal dynasty" .)