Pub’s first of eight in immediate area (6)
I believe the answer is:
locale
'immediate area' is the definition.
(a local area)
'pub's first of eight' is the wordplay.
'pub' becomes 'local' (one's local pub).
'first of eight' becomes 'e' (1st letter of 'eight').
'local'+'e'='LOCALE'
'in' acts as a link.
(Other definitions for locale that I've seen before include "Scene of event or occurrence" , "Area connected with event" , "Spot" , "Venue" , "where something happens" .)