Dog’s had a heart transplant? Goodness me! (3)
I believe the answer is:
cor
'goodness me' is the definition.
(both are expressions of surprise)
'dog's had a heart transplant?' is the wordplay.
'dog's had' becomes 'c' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'a heart' means to look at the middle letters.
'transplant?' becomes 'work' (transplant is a kind of work).
The central letters of 'work' are 'or'.
'c'+'or'='COR'
(Other definitions for cor that I've seen before include "Expression of surprise" , "Surprised expression" , "Blimey" , "Gosh" .)