The British heart transplant girl (6)
I believe the answer is:
bertha
'girl' is the definition.
'the british heart transplant' is the wordplay.
'the british' becomes 'b' (abbreviation e.g. in 'BBC').
'transplant' indicates anagramming the letters.
'heart' is an anagram of 'ertha'.
'b'+'ertha'='BERTHA'
(Other definitions for bertha that I've seen before include "collar" , "Big - - , WW1 gun" , "big woman?" , "Girl's name - big German WWI gun" , "Female name; Big -, World War one German howitzer" .)