Beef gone, sheep beginning to increase (8)
I believe the answer is:
pastrami
'beef' is the definition.
(I know that Pastrami is a type of beef)
'gone sheep beginning to increase' is the wordplay.
'gone' becomes 'past' (similar in meaning).
'sheep' becomes 'ram' (male sheep).
'beginning to' suggests taking the first letters.
The initial letter of 'increase' is 'i'.
'past'+'ram'+'i'='PASTRAMI'
(Other definitions for pastrami that I've seen before include "Thinly sliced beef" , "Spicy smoked beef" , "Meat dish" , "Highly seasoned cut of smoked beef" , "Seasoned dish" .)