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Meat from a deli’s former branches (8)

Ross

I believe the answer is:

pastrami

I'm a little stuck... Click here to teach me more about this clue!

'meat from a deli's' is the definition.
'pastrami' can be an answer for 'meat' (pastrami is a kind of meat). I am not certain of the 'from a deli's' bit.

'former branches' is the wordplay.
'former' becomes 'past' (similar in meaning).
'branches' becomes 'rami' (I've seen this in another clue).
'past'+'rami'='PASTRAMI'

Can you help me to learn more?

(Other definitions for pastrami that I've seen before include "Spiced sliced beef" , "Meat dish" , "Highly seasoned cut of smoked beef" , "Spiced smoked beef" , "Spicy smoked beef" .)

I've seen this clue in The Sunday Times.
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