District with central area and private central zone (6)
I believe the answer is:
region
'district' is the definition.
(I know that district can be written as region)
'central area and private central zone' is the wordplay.
'central' says to take the centre.
'and' says to put letters next to each other.
'private' becomes 'GI' (GI can informally mean a US soldier).
'central' indicates the central letters.
The middle of 'area' is 're'.
The central letters of 'zone' are 'on'.
're'+'gi'+'on'='REGION'
'with' acts as a link.
(Other definitions for region that I've seen before include "Ignore (anag) - area" , "Area, territory" , "Area of country" , "Area, domain" , "Kind of territory to ignore" .)