Bone in back and middle of rump (7)
I believe the answer is:
sternum
'bone' is the definition.
(the breastbone)
'back and middle of rump' is the wordplay.
'back' becomes 'stern' (stern means the back of a boat).
'and' is a charade indicator (letters next to each other).
'middle of' means to look at the middle letters.
The middle letters of 'rump' are 'um'.
'stern'+'um'='STERNUM'
'in' acts as a link.
(Other definitions for sternum that I've seen before include "Breastbone" , "Chest bone" , "Munster (anag.)" , "front of breast" , "Human bone -- ten rums (anag)" .)