Grandma’s sister having change of heart (3)

I believe the answer is:

nan

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'grandma's' is the definition.
(I've seen this in other clues)

'sister having change of heart' is the wordplay.
'sister' becomes 'n' (I can't justify this - if you can you should believe this answer much more).
'having' means one lot of letters go next to another.
'of heart' indicates the central letters (I've seen 'heart of' mean this).
The middle letters of 'change' are 'an'.
'n'+'an'='NAN'

Can you help me to learn more?

(Other definitions for nan that I've seen before include "Grandmother (colloq.)" , "Indian bread; grandma" , "Granny; bread" , "Relation" , "A relative (colloq.); unleavened bread" .)

I've seen this clue in The Times.

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