Large following abandoning central pub (5)
I believe the answer is:
Here is my best explanation:
'pub' is the definition.
(I've seen this before)
'large following abandoning central' is the subsidiary indication.
'large' becomes 'l'.
'following' becomes 'f' (abbreviation listed in Chambers).
'abandoning' suggests deleting specific letters.
'central' becomes 'focal' ('focal' can be similar in meaning to 'central').
'focal' with 'f' removed is 'ocal'.
(Other definitions for local that I've seen before include "Regional; a pub", "Your friendly neighbourhood pub", "Nearest pub", "Relating to the neighbourhood", "Nieghbourhood pub or its customer", "One won't knock you out", "The familiar neighbourhood pub", "round the corner", "One's nearest pub" and "Convenient pub".)