One after old sheep meat (8)
I believe the answer is:
pastrami
'meat' is the definition.
(pastrami is a kind of meat)
'one after old sheep' is the wordplay.
'one' becomes 'i' (Roman numeral).
'after' is a charade indicator (letters next to each other).
'old' becomes 'past' ('past' can be similar in meaning to 'old').
'sheep' becomes 'ram' (ram is a kind of sheep).
'past'+'ram'='pastram'
'i' after 'pastram' is 'PASTRAMI'.
(Other definitions for pastrami that I've seen before include "Highly seasoned cut of smoked beef" , "Seasoned dish" , "A tramp is (anag) - meat" , "Spiced smoked beef" , "Meat dish" .)