Children regularly rejected your pizza (old sausage) (7)
I believe the answer is:
chorizo
'sausage' is the definition.
(type of sausage)
'children regularly rejected your pizza old' is the wordplay.
'children' becomes 'ch' (genealogical abbreviation).
'regularly rejected' means one should take alternating letters.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'your'+'pizza'='yourpizza'
The alternate letters of 'yourpizza' are 'oriz'.
'ch'+'oriz'+'o'='CHORIZO'
(Other definitions for chorizo that I've seen before include "Spiced sausage" , "Hot sausage" , "Spicy Spanish meat product" , "foreign meat" , "food from the deli" .)