Piece of pork over -- starts to reheat it on top of barbecue (5,3)
I believe the answer is:
spare rib
'piece of pork' is the definition.
(pork rib)
'over starts to reheat it on top of barbecue' is the wordplay.
'over' becomes 'spare' (I've seen this before).
'starts to' indicates taking the first letters.
'on top of' says to take the initial letters.
The initial letters of 'reheat it' is 'ri'.
The initial letter of 'barbecue' is 'b'.
'spare'+'ri'+'b'='SPARE-RIB'
(Other definitions for spare rib that I've seen before include "it's hardly a chop)" , "piece of pork" , "Only a little pork on this bone" , "Meat on the bone served in barbecue sauce" , "Bony pork serving" .)