Local people’s unusually big heads (3)
I believe the answer is:
pub
'local' is the definition.
(thesaurus)
'people's unusually big heads' is the wordplay.
'heads' says to take the initial letters.
The initial letters of 'peoples unusually big' is 'PUB'.
(Other definitions for pub that I've seen before include "Inn, tavern" , "A familiar hostelry" , "The humble local tavern" , "Slug and Lettuce, perhaps" , "Tavern, hostelry" .)