Do out pub and be prompt (8)

I believe the answer is:

barbecue

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But I can't explain it at all! Could you help me understand?

(Other definitions for barbecue that I've seen before include "Cuba beer for outdoor meat meal" , "A picnic with grilled meats" , "outdoor catering" , "Grill for outdoor cooking" , "Cook on an open fire" .)

I've seen this clue in The Sun.

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