New prince eating old, old cheese (8)
I believe the answer is:
pecorino
'cheese' is the definition.
(I've seen this before)
'new prince eating old old' is the wordplay.
'new' indicates an anagram.
'eating' is an insertion indicator.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'prince' with letters rearranged gives 'pecrin'.
'pecrin' going around 'o' is 'pecorin'.
'pecorin'+'o'='PECORINO'
(Other definitions for pecorino that I've seen before include "Italian sheep's cheese" , "Italian cheese made from ewe's milk" , "Hard cheese!" .)