Refuse originally found in old Cornish river (5)
I believe the answer is:
offal
'refuse' is the definition.
(thesaurus)
'originally found in old cornish river' is the wordplay.
'originally' suggests taking the first letters.
'in' means one lot of letters goes inside another.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'cornish river' becomes 'fal' (River Fal).
The first letter of 'found' is 'f'.
'o'+'fal'='ofal'
'f' inserted into 'ofal' is 'OFFAL'.
(Other definitions for offal that I've seen before include "Liver or tongue, for example" , "Waste of carcase" , "Edible (or inedible?) internal organs" , "Internal organs of an animal used as food" , "Edible liver or heart of animal" .)